[{"ddc":["515"],"doi_confirm":"1","citation":{"ieee":"Y. Li, “Spectral rigidity and nonrigidity of dynamical systems,” Institute of Science and Technology Austria, 2026.","chicago":"Li, Yunzhe. “Spectral Rigidity and Nonrigidity of Dynamical Systems.” Institute of Science and Technology Austria, 2026. <a href=\"https://doi.org/10.15479/AT-ISTA-22255\">https://doi.org/10.15479/AT-ISTA-22255</a>.","ama":"Li Y. Spectral rigidity and nonrigidity of dynamical systems. 2026. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-22255\">10.15479/AT-ISTA-22255</a>","mla":"Li, Yunzhe. <i>Spectral Rigidity and Nonrigidity of Dynamical Systems</i>. Institute of Science and Technology Austria, 2026, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-22255\">10.15479/AT-ISTA-22255</a>.","short":"Y. Li, Spectral Rigidity and Nonrigidity of Dynamical Systems, Institute of Science and Technology Austria, 2026.","apa":"Li, Y. (2026). <i>Spectral rigidity and nonrigidity of dynamical systems</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-22255\">https://doi.org/10.15479/AT-ISTA-22255</a>","ista":"Li Y. 2026. Spectral rigidity and nonrigidity of dynamical systems. Institute of Science and Technology Austria."},"abstract":[{"text":"This thesis studies spectral rigidity and nonrigidity phenomena in dynamical systems. The central question is whether a dynamical system can be determined, up to a natural conjugacy, from its spectrum. We consider three related spectra: the length spectrum, the action spectrum, and the Lyapunov spectrum.\r\n\r\nThe first part of the thesis concerns Liouville metrics on the two-dimensional torus. It is a long-standing folklore conjecture that Liouville metrics are the only integrable metrics on the torus. We prove a length-spectral rigidity result for linear conformal deformations of Liouville metrics by exploiting the dynamical properties of the rational tori -- analogues of the resonant convex caustics in billiards. We also establish a complementary classification result showing that marked-length-isospectral Liouville metrics are characterized by rearrangements of the one-dimensional functions appearing in their conformal factors, generalizing a theorem of Abbondandolo-Mazzucchelli. In particular, the second result gives nonrigidity examples within the class of Liouville metrics.\r\n\r\nThe second part of the thesis studies the standard map from the viewpoint of action and Lyapunov spectra. We construct nontrivial deformations of the standard map which preserve the symplectic actions (respectively, the Lyapunov exponents) of infinitely many periodic orbits accumulating on an invariant curve. The proof combines a resonant normal form construction with Picard iteration schemes to obtain a sequence of periodic orbits accumulating on an invariant curve with a Liouville rotation number. Within the resonant normal forms we capture the dependence of these periodic orbits on the resonant Fourier coefficients of the dynamics on the invariant curve and, using the contraction mapping principle, obtain a suitable deformation achieving the prescribed spectral data associated with this sequence of orbits. The result can be viewed as a symplectic twist-map analogue of a length-spectral nonrigidity phenomenon for Riemannian manifolds and convex billiards, and it motivates the existence problem for similar 'partially length-isospectral' deformations of strictly convex billiard tables.\r\n","lang":"eng"}],"day":"11","page":"131","month":"07","oa":1,"publisher":"Institute of Science and Technology Austria","department":[{"_id":"GradSch"},{"_id":"VaKa"}],"OA_place":"publisher","publication_status":"published","file_date_updated":"2026-07-20T14:00:33Z","article_processing_charge":"No","related_material":{"record":[{"relation":"part_of_dissertation","id":"22340","status":"public"},{"status":"public","id":"22341","relation":"part_of_dissertation"}]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"has_accepted_license":"1","title":"Spectral rigidity and nonrigidity of dynamical systems","degree_awarded":"PhD","_id":"22255","corr_author":"1","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","type":"dissertation","acknowledgement":"The financial support of the ERC grant SPERIG #885707 is gratefully acknowledged.\r\n","project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707","call_identifier":"H2020"}],"file":[{"date_created":"2026-07-14T10:48:45Z","creator":"yli","relation":"main_file","file_name":"2026_Li_Yunzhe_Thesis.pdf","file_size":1260717,"checksum":"8201cb5a427656a41828ecde8a85c04b","date_updated":"2026-07-14T10:48:45Z","access_level":"open_access","content_type":"application/pdf","file_id":"22337"},{"date_created":"2026-07-14T11:07:18Z","relation":"source_file","creator":"yli","file_name":"2026_Li_Yunzhe_Thesis.zip","file_size":418752,"checksum":"19ee8461ed77f5b7980fc9461f778b6f","date_updated":"2026-07-20T14:00:33Z","content_type":"application/x-zip-compressed","access_level":"closed","file_id":"22339"}],"date_created":"2026-07-08T12:44:31Z","ec_funded":1,"date_published":"2026-07-11T00:00:00Z","date_updated":"2026-07-20T14:58:23Z","year":"2026","supervisor":[{"orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim"}],"publication_identifier":{"issn":["2663-337X"]},"author":[{"id":"41cb05d3-f128-11eb-9611-e4e2b3cfba31","last_name":"Li","first_name":"Yunzhe","full_name":"Li, Yunzhe"}],"doi":"10.15479/AT-ISTA-22255","oa_version":"Published Version","acknowledged_ssus":[{"_id":"E-Lib"},{"_id":"CampIT"}],"alternative_title":["ISTA Thesis"],"language":[{"iso":"eng"}],"status":"public"},{"external_id":{"arxiv":["2111.12171"]},"file":[{"relation":"main_file","creator":"dernst","file_size":2256345,"file_name":"2026_InventionesMath_Koval.pdf","date_created":"2026-07-23T10:55:24Z","success":1,"date_updated":"2026-07-23T10:55:24Z","content_type":"application/pdf","access_level":"open_access","file_id":"22394","checksum":"487fa9113e1bbf32a6c70e6d1e8f63bc"}],"date_created":"2023-09-06T08:35:43Z","date_published":"2026-04-01T00:00:00Z","OA_type":"hybrid","ec_funded":1,"year":"2026","date_updated":"2026-07-23T10:58:59Z","author":[{"full_name":"Koval, Illya","last_name":"Koval","id":"2eed1f3b-896a-11ed-bdf8-93c7c4bf159e","first_name":"Illya"}],"publication":"Inventiones Mathematicae","publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"quality_controlled":"1","oa_version":"Published Version","doi":"10.1007/s00222-025-01397-y","status":"public","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"mathsc":["37C83","35J05","37J70","74J25"],"has_accepted_license":"1","_id":"14278","title":"Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","type":"journal_article","acknowledgement":"The author acknowledges the partial support of the European Research Council Grant #885707. He also thanks Vadim Kaloshin for proposing the idea of the project and greatly aiding the implementation. The author is also grateful to Hamid Hezari, Amir Vig, Steve Zelditch, Comlan E. Koudjinan, Corentin Fierobe, Ngo Nhok Tkhai Shon and Roman Sarapin for useful discussions. The author also acknowledges partial support of ISTern summer program. The project started in the summer of 2021, when the author was an intern at ISTA. Open access funding provided by Institute of Science and Technology (IST Austria).","volume":244,"PlanS_conform":"1","project":[{"call_identifier":"H2020","name":"Spectral rigidity and integrability for billiards and geodesic flows","grant_number":"885707","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A"}],"arxiv":1,"intvolume":"       244","publisher":"Springer Nature","researchdata_availability":"no","das_tickbox":"0","department":[{"_id":"GradSch"},{"_id":"VaKa"}],"publication_status":"published","OA_place":"publisher","file_date_updated":"2026-07-23T10:55:24Z","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","ddc":["510"],"article_type":"original","citation":{"mla":"Koval, Illya. “Local Strong Birkhoff Conjecture and Local Spectral Rigidity of Almost Every Ellipse.” <i>Inventiones Mathematicae</i>, vol. 244, Springer Nature, 2026, pp. 221–98, doi:<a href=\"https://doi.org/10.1007/s00222-025-01397-y\">10.1007/s00222-025-01397-y</a>.","ieee":"I. Koval, “Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse,” <i>Inventiones Mathematicae</i>, vol. 244. Springer Nature, pp. 221–298, 2026.","ama":"Koval I. Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse. <i>Inventiones Mathematicae</i>. 2026;244:221-298. doi:<a href=\"https://doi.org/10.1007/s00222-025-01397-y\">10.1007/s00222-025-01397-y</a>","chicago":"Koval, Illya. “Local Strong Birkhoff Conjecture and Local Spectral Rigidity of Almost Every Ellipse.” <i>Inventiones Mathematicae</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00222-025-01397-y\">https://doi.org/10.1007/s00222-025-01397-y</a>.","short":"I. Koval, Inventiones Mathematicae 244 (2026) 221–298.","ista":"Koval I. 2026. Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse. Inventiones Mathematicae. 244, 221–298.","apa":"Koval, I. (2026). Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-025-01397-y\">https://doi.org/10.1007/s00222-025-01397-y</a>"},"abstract":[{"lang":"eng","text":"The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrability, namely, integrability close to the boundary, and prove a local version of this conjecture: a small perturbation of almost every ellipse that preserves integrability near the boundary, is itself an ellipse. We apply this result to study local spectral uniqueness of ellipses using the connection between the wave trace of the Laplacian and the dynamics near the boundary and establish local uniqueness for almost all of them."}],"day":"01","page":"221-298","month":"04","supplementarymaterial":"yes","oa":1},{"publisher":"EMS Press","DOAJ_listed":"1","publication_status":"epub_ahead","OA_place":"publisher","department":[{"_id":"VaKa"}],"scopus_import":"1","article_processing_charge":"Yes","article_type":"original","ddc":["500"],"citation":{"mla":"Helfter, Mathieu. “Sets with Arbitrary Hausdorff and Packing Scales in Infinite Dimensional Banach Spaces.” <i>Journal of Fractal Geometry</i>, EMS Press, 2025, doi:<a href=\"https://doi.org/10.4171/jfg/177\">10.4171/jfg/177</a>.","ama":"Helfter M. Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces. <i>Journal of Fractal Geometry</i>. 2025. doi:<a href=\"https://doi.org/10.4171/jfg/177\">10.4171/jfg/177</a>","chicago":"Helfter, Mathieu. “Sets with Arbitrary Hausdorff and Packing Scales in Infinite Dimensional Banach Spaces.” <i>Journal of Fractal Geometry</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/jfg/177\">https://doi.org/10.4171/jfg/177</a>.","ieee":"M. Helfter, “Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces,” <i>Journal of Fractal Geometry</i>. EMS Press, 2025.","apa":"Helfter, M. (2025). Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces. <i>Journal of Fractal Geometry</i>. EMS Press. <a href=\"https://doi.org/10.4171/jfg/177\">https://doi.org/10.4171/jfg/177</a>","ista":"Helfter M. 2025. Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces. Journal of Fractal Geometry.","short":"M. Helfter, Journal of Fractal Geometry (2025)."},"abstract":[{"text":"For every couple of Hausdorff functions ψ and φ verifying some mild assumptions, there exists a compact subset K of the Baire space such that the φ-Hausdorff measure and the ψ-packing measure on K are both finite and positive. Such examples are then embedded in any infinite dimensional Banach space to answer positively a question of Fan on the existence of metric spaces with arbitrary scales.","lang":"eng"}],"day":"07","month":"11","main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/jfg/177"}],"oa":1,"date_created":"2025-12-19T10:15:37Z","OA_type":"gold","date_published":"2025-11-07T00:00:00Z","year":"2025","date_updated":"2026-06-18T18:26:33Z","publication":"Journal of Fractal Geometry","publication_identifier":{"issn":["2308-1309"],"eissn":["2308-1317"]},"author":[{"last_name":"Helfter","full_name":"Helfter, Mathieu","id":"7d296fbe-e2c6-11ee-84d3-d5c2945f9a57","first_name":"Mathieu"}],"oa_version":"Published Version","doi":"10.4171/jfg/177","quality_controlled":"1","language":[{"iso":"eng"}],"status":"public","title":"Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces","_id":"20839","corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article"},{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2206.05231","open_access":"1"}],"month":"05","oa":1,"abstract":[{"text":"We introduce the notions of scale for sets and measures on metric space by generalizing the usual notions of dimension. Several versions of scales are introduced such as Hausdorff, packing, box, local and quantization. They are defined for different growth, allowing a refined study of infinite dimensional spaces. We prove general theorems comparing the different versions of scales. They are applied to describe geometries of ergodic decompositions, of the Wiener measure and from functional spaces. The first application solves a problem of Berger on the notions of emergence (2020); the second lies in the geometry of the Wiener measure and extends the work of Dereich–Lifshits (2005); the last refines Kolmogorov–Tikhomirov (1958) study on finitely differentiable functions.","lang":"eng"}],"citation":{"short":"M. Helfter, Mathematische Zeitschrift 310 (2025).","ista":"Helfter M. 2025. Scales. Mathematische Zeitschrift. 310, 15.","apa":"Helfter, M. (2025). Scales. <i>Mathematische Zeitschrift</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00209-025-03719-5\">https://doi.org/10.1007/s00209-025-03719-5</a>","ieee":"M. Helfter, “Scales,” <i>Mathematische Zeitschrift</i>, vol. 310. Springer Nature, 2025.","ama":"Helfter M. Scales. <i>Mathematische Zeitschrift</i>. 2025;310. doi:<a href=\"https://doi.org/10.1007/s00209-025-03719-5\">10.1007/s00209-025-03719-5</a>","chicago":"Helfter, Mathieu. “Scales.” <i>Mathematische Zeitschrift</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00209-025-03719-5\">https://doi.org/10.1007/s00209-025-03719-5</a>.","mla":"Helfter, Mathieu. “Scales.” <i>Mathematische Zeitschrift</i>, vol. 310, 15, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00209-025-03719-5\">10.1007/s00209-025-03719-5</a>."},"article_type":"original","day":"01","OA_place":"repository","department":[{"_id":"VaKa"}],"publication_status":"published","article_processing_charge":"No","scopus_import":"1","article_number":"15","publisher":"Springer Nature","intvolume":"       310","isi":1,"type":"journal_article","volume":310,"arxiv":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","_id":"19496","title":"Scales","author":[{"last_name":"Helfter","id":"7d296fbe-e2c6-11ee-84d3-d5c2945f9a57","first_name":"Mathieu","full_name":"Helfter, Mathieu"}],"publication":"Mathematische Zeitschrift","publication_identifier":{"issn":["0025-5874"],"eissn":["1432-1823"]},"year":"2025","date_updated":"2025-09-30T11:31:00Z","status":"public","language":[{"iso":"eng"}],"quality_controlled":"1","doi":"10.1007/s00209-025-03719-5","oa_version":"Preprint","external_id":{"isi":["001450830300001"],"arxiv":["2206.05231"]},"date_published":"2025-05-01T00:00:00Z","OA_type":"green","date_created":"2025-04-06T22:01:32Z"},{"intvolume":"        35","publisher":"Springer Nature","department":[{"_id":"VaKa"}],"publication_status":"published","OA_place":"publisher","file_date_updated":"2025-12-30T09:28:58Z","article_number":"306","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","article_type":"original","ddc":["510"],"citation":{"short":"D. Tsodikovich, Journal of Geometric Analysis 35 (2025).","ista":"Tsodikovich D. 2025. Local rigidity for symplectic billiards. Journal of Geometric Analysis. 35(10), 306.","apa":"Tsodikovich, D. (2025). Local rigidity for symplectic billiards. <i>Journal of Geometric Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s12220-025-02148-4\">https://doi.org/10.1007/s12220-025-02148-4</a>","mla":"Tsodikovich, Daniel. “Local Rigidity for Symplectic Billiards.” <i>Journal of Geometric Analysis</i>, vol. 35, no. 10, 306, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s12220-025-02148-4\">10.1007/s12220-025-02148-4</a>.","ama":"Tsodikovich D. Local rigidity for symplectic billiards. <i>Journal of Geometric Analysis</i>. 2025;35(10). doi:<a href=\"https://doi.org/10.1007/s12220-025-02148-4\">10.1007/s12220-025-02148-4</a>","chicago":"Tsodikovich, Daniel. “Local Rigidity for Symplectic Billiards.” <i>Journal of Geometric Analysis</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s12220-025-02148-4\">https://doi.org/10.1007/s12220-025-02148-4</a>.","ieee":"D. Tsodikovich, “Local rigidity for symplectic billiards,” <i>Journal of Geometric Analysis</i>, vol. 35, no. 10. Springer Nature, 2025."},"abstract":[{"lang":"eng","text":"We show a local rigidity result for the integrability of symplectic billiards. We prove that any domain which is close to an ellipse, and for which the symplectic billiard map is rationally integrable must be an ellipse as well. This is in spirit of the result of [2] for Birkhoff billiards."}],"day":"07","month":"08","oa":1,"external_id":{"isi":["001546433200002"],"arxiv":["2501.08849"]},"date_created":"2025-08-17T22:01:35Z","file":[{"date_updated":"2025-12-30T09:28:58Z","content_type":"application/pdf","access_level":"open_access","file_id":"20907","checksum":"ed86500742b3fd93db3287558a630383","relation":"main_file","creator":"dernst","file_name":"2025_JourGeomAnalysis_Tsodikovich.pdf","file_size":484344,"date_created":"2025-12-30T09:28:58Z","success":1}],"ec_funded":1,"OA_type":"hybrid","date_published":"2025-08-07T00:00:00Z","date_updated":"2025-12-30T09:29:27Z","year":"2025","publication":"Journal of Geometric Analysis","publication_identifier":{"issn":["1050-6926"]},"author":[{"id":"04531810-fb3e-11ef-87f0-800a4ce333db","full_name":"Tsodikovich, Daniel","last_name":"Tsodikovich","first_name":"Daniel"}],"doi":"10.1007/s12220-025-02148-4","oa_version":"Published Version","quality_controlled":"1","language":[{"iso":"eng"}],"status":"public","issue":"10","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"has_accepted_license":"1","title":"Local rigidity for symplectic billiards","_id":"20185","corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"The author would like to thank Corentin Fierobe, Vadim Kaloshin, Illya Koval and Yunzhe Li for useful discussions. The author would also like to thank the referee for useful remarks. Open access funding provided by Institute of Science and Technology (IST Austria). European Research Council (885707) Mr Daniel Tsodikovich","type":"journal_article","volume":35,"isi":1,"PlanS_conform":"1","project":[{"_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707","name":"Spectral rigidity and integrability for billiards and geodesic flows","call_identifier":"H2020"}],"arxiv":1},{"keyword":["Differential Geometry (math.DG)","Mathematical Physics (math-ph)","Dynamical Systems (math.DS)","Spectral Theory (math.SP)","FOS: Mathematics","FOS: Mathematics","FOS: Physical sciences","FOS: Physical sciences","58J42","37J35","37J35","35P20","58J40","58J50","37D40"],"article_processing_charge":"No","department":[{"_id":"VaKa"},{"_id":"LaEr"}],"OA_place":"repository","publication_status":"draft","day":"13","citation":{"ista":"Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori. arXiv, <a href=\"https://doi.org/10.48550/ARXIV.2511.10398\">10.48550/ARXIV.2511.10398</a>.","apa":"Henheik, S. J., Kaloshin, V., Li, Y., &#38; Vig, A. (n.d.). Spectral rigidity of Liouville tori. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2511.10398\">https://doi.org/10.48550/ARXIV.2511.10398</a>","short":"S.J. Henheik, V. Kaloshin, Y. Li, A. Vig, ArXiv (n.d.).","chicago":"Henheik, Sven Joscha, Vadim Kaloshin, Yunzhe Li, and Amir Vig. “Spectral Rigidity of Liouville Tori.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2511.10398\">https://doi.org/10.48550/ARXIV.2511.10398</a>.","ama":"Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2511.10398\">10.48550/ARXIV.2511.10398</a>","ieee":"S. J. Henheik, V. Kaloshin, Y. Li, and A. Vig, “Spectral rigidity of Liouville tori,” <i>arXiv</i>. .","mla":"Henheik, Sven Joscha, et al. “Spectral Rigidity of Liouville Tori.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/ARXIV.2511.10398\">10.48550/ARXIV.2511.10398</a>."},"abstract":[{"lang":"eng","text":"We show that Laplace isospectral deformations within a conformal class of generic Liouville metrics on the two-dimensional torus that are linear in the deformation parameter are necessarily trivial. Two of the main ingredients in our proof are a noncancellation result for the wave trace and an analysis of the second order variational formula for the energy functional associated to closed geodesics. Noncancellation allows us to detect parts of the length spectrum from the Laplace spectrum and conclude rational integrability for the deformed geodesic flow (Liouville metrics are folklorically conjectured to be the only Riemannian metrics with integrable geodesic flow on the torus). We then use the second variational formula to show how the preservation of a single rational torus is sufficient to conclude triviality of the deformation, assuming linearity. We also present some evidence that our hypothesis of linearity may indeed be necessary."}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2511.10398"}],"month":"11","OA_type":"green","date_published":"2025-11-13T00:00:00Z","date_created":"2026-07-14T12:51:50Z","external_id":{"arxiv":["2511.10398"]},"language":[{"iso":"eng"}],"status":"public","doi":"10.48550/ARXIV.2511.10398","oa_version":"Preprint","publication":"arXiv","author":[{"first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","orcid":"0000-0003-1106-327X"},{"last_name":"Kaloshin","first_name":"Vadim","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628"},{"first_name":"Yunzhe","id":"41cb05d3-f128-11eb-9611-e4e2b3cfba31","last_name":"Li","full_name":"Li, Yunzhe"},{"full_name":"Vig, Amir","last_name":"Vig","first_name":"Amir","id":"49d58dd5-45f5-11ec-9f86-8ce1276989b9"}],"date_updated":"2026-07-20T14:58:23Z","year":"2025","corr_author":"1","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","title":"Spectral rigidity of Liouville tori","_id":"22340","related_material":{"record":[{"id":"22255","relation":"dissertation_contains","status":"public"}]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"arxiv":1,"type":"preprint"},{"day":"03","citation":{"short":"Y. Li, ArXiv (n.d.).","ista":"Li Y. Deformations of the standard map with prescribed actions and Lyapunov exponents. arXiv, <a href=\"https://doi.org/10.48550/ARXIV.2512.03865\">10.48550/ARXIV.2512.03865</a>.","apa":"Li, Y. (n.d.). Deformations of the standard map with prescribed actions and Lyapunov exponents. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2512.03865\">https://doi.org/10.48550/ARXIV.2512.03865</a>","ama":"Li Y. Deformations of the standard map with prescribed actions and Lyapunov exponents. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2512.03865\">10.48550/ARXIV.2512.03865</a>","ieee":"Y. Li, “Deformations of the standard map with prescribed actions and Lyapunov exponents,” <i>arXiv</i>. .","chicago":"Li, Yunzhe. “Deformations of the Standard Map with Prescribed Actions and Lyapunov Exponents.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2512.03865\">https://doi.org/10.48550/ARXIV.2512.03865</a>.","mla":"Li, Yunzhe. “Deformations of the Standard Map with Prescribed Actions and Lyapunov Exponents.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/ARXIV.2512.03865\">10.48550/ARXIV.2512.03865</a>."},"abstract":[{"lang":"eng","text":"We construct nontrivial deformations of the standard map which preserve the symplectic actions, respectively the Lyapunov exponents, of infinitely many periodic orbits accumulating to an invariant curve. The proof uses a resonant normal-form construction to obtain a sequence of periodic orbits accumulating on an invariant curve with a Liouville rotation number. Within these normal forms we capture the dependence of these periodic orbits on the resonant Fourier coefficients of the dynamics on the invariant curve and, using the contraction mapping principle, obtain a suitable deformation achieving the prescribed spectral data associated with this sequence of orbits. The result can be viewed as a symplectic twist-map analogue of a length spectral nonrigidity phenomenon for Riemannian manifolds and convex billiards, and it motivates the existence problem for similar 'partially length-isospectral' deformations of strictly convex billiard tables."}],"oa":1,"month":"12","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2512.03865"}],"keyword":["Dynamical Systems (math.DS)","FOS: Mathematics","FOS: Mathematics"],"article_processing_charge":"No","department":[{"_id":"VaKa"}],"publication_status":"draft","OA_place":"repository","title":"Deformations of the standard map with prescribed actions and Lyapunov exponents","_id":"22341","corr_author":"1","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","related_material":{"record":[{"id":"22255","relation":"dissertation_contains","status":"public"}]},"arxiv":1,"project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","grant_number":"885707","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","call_identifier":"H2020"}],"acknowledgement":" The author would like to thank Vadim Kaloshin for initiating this project and for his guidance throughout its development. The author also\r\nthanks Abed Bounemoura, Bassam Fayad, Mathieu Helfter, Comlan Edmond Koudjinan, Illya Koval, Yi Pan, and Daniel Tsodikovich for many helpful discussions. The\r\nfinancial support of the ERC grant SPERIG #885707 is gratefully acknowledged.","type":"preprint","date_created":"2026-07-14T13:02:29Z","ec_funded":1,"OA_type":"green","date_published":"2025-12-03T00:00:00Z","external_id":{"arxiv":["2512.03865"]},"oa_version":"Preprint","doi":"10.48550/ARXIV.2512.03865","language":[{"iso":"eng"}],"status":"public","date_updated":"2026-07-20T14:58:23Z","year":"2025","publication":"arXiv","author":[{"full_name":"Li, Yunzhe","last_name":"Li","id":"41cb05d3-f128-11eb-9611-e4e2b3cfba31","first_name":"Yunzhe"}]},{"isi":1,"volume":34,"type":"journal_article","acknowledgement":"We are grateful to the anonymous referee for their careful reading and valuable remarks and comments which helped to improve significantly the paper. Open access funding provided by Institute of Science and Technology (IST Austria). V.K. and C.E.K. gratefully acknowledge support from the European Research Council (ERC) through the Advanced Grant “SPERIG” (#885 707).","project":[{"call_identifier":"H2020","grant_number":"885707","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","name":"Spectral rigidity and integrability for billiards and geodesic flows"}],"arxiv":1,"has_accepted_license":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","_id":"18483","title":"Birkhoff conjecture for nearly centrally symmetric domains","author":[{"full_name":"Kaloshin, Vadim","last_name":"Kaloshin","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628"},{"full_name":"Koudjinan, Edmond","first_name":"Edmond","last_name":"Koudjinan","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","orcid":"0000-0003-2640-4049"},{"last_name":"Zhang","full_name":"Zhang, Ke","first_name":"Ke"}],"publication":"Geometric and Functional Analysis","publication_identifier":{"issn":["1016-443X"],"eissn":["1420-8970"]},"year":"2024","date_updated":"2025-09-08T14:27:45Z","status":"public","language":[{"iso":"eng"}],"quality_controlled":"1","oa_version":"Published Version","doi":"10.1007/s00039-024-00695-6","external_id":{"isi":["001329804200001"],"arxiv":["2306.12301"]},"date_published":"2024-12-01T00:00:00Z","ec_funded":1,"OA_type":"hybrid","date_created":"2024-10-27T23:01:45Z","file":[{"checksum":"e7fcd9f78beb40408c7d858ac0625e27","file_id":"18833","date_updated":"2025-01-13T09:14:24Z","access_level":"open_access","content_type":"application/pdf","success":1,"date_created":"2025-01-13T09:14:24Z","creator":"dernst","relation":"main_file","file_size":2260980,"file_name":"2024_GeometricFunctionalAnalysis_Kaloshin.pdf"}],"month":"12","oa":1,"abstract":[{"text":"In this paper we prove a perturbative version of a remarkable Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) result. They prove non perturbative Birkhoff conjecture for centrally-symmetric convex domains, namely, a centrally-symmetric convex domain with integrable billiard is ellipse. We combine techniques from Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) with a local result by Kaloshin–Sorrentino (Ann. Math. 188(1):315–380, 2018) and show that a domain close enough to a centrally symmetric one with integrable billiard is ellipse. To combine these results we derive a slight extension of Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) by proving that a notion of rational integrability is equivalent to the C0-integrability condition used in their paper.","lang":"eng"}],"citation":{"mla":"Kaloshin, Vadim, et al. “Birkhoff Conjecture for Nearly Centrally Symmetric Domains.” <i>Geometric and Functional Analysis</i>, vol. 34, Springer Nature, 2024, pp. 1973–2007, doi:<a href=\"https://doi.org/10.1007/s00039-024-00695-6\">10.1007/s00039-024-00695-6</a>.","chicago":"Kaloshin, Vadim, Edmond Koudjinan, and Ke Zhang. “Birkhoff Conjecture for Nearly Centrally Symmetric Domains.” <i>Geometric and Functional Analysis</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00039-024-00695-6\">https://doi.org/10.1007/s00039-024-00695-6</a>.","ama":"Kaloshin V, Koudjinan E, Zhang K. Birkhoff conjecture for nearly centrally symmetric domains. <i>Geometric and Functional Analysis</i>. 2024;34:1973-2007. doi:<a href=\"https://doi.org/10.1007/s00039-024-00695-6\">10.1007/s00039-024-00695-6</a>","ieee":"V. Kaloshin, E. Koudjinan, and K. Zhang, “Birkhoff conjecture for nearly centrally symmetric domains,” <i>Geometric and Functional Analysis</i>, vol. 34. Springer Nature, pp. 1973–2007, 2024.","ista":"Kaloshin V, Koudjinan E, Zhang K. 2024. Birkhoff conjecture for nearly centrally symmetric domains. Geometric and Functional Analysis. 34, 1973–2007.","apa":"Kaloshin, V., Koudjinan, E., &#38; Zhang, K. (2024). Birkhoff conjecture for nearly centrally symmetric domains. <i>Geometric and Functional Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00039-024-00695-6\">https://doi.org/10.1007/s00039-024-00695-6</a>","short":"V. Kaloshin, E. Koudjinan, K. Zhang, Geometric and Functional Analysis 34 (2024) 1973–2007."},"ddc":["510"],"article_type":"original","page":"1973-2007","day":"01","file_date_updated":"2025-01-13T09:14:24Z","department":[{"_id":"VaKa"}],"OA_place":"publisher","publication_status":"published","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","publisher":"Springer Nature","intvolume":"        34"},{"oa_version":"Preprint","doi":"10.30757/ALEA.V21-70","quality_controlled":"1","language":[{"iso":"eng"}],"status":"public","issue":"2","year":"2024","date_updated":"2025-09-08T14:48:42Z","publication":"Alea","publication_identifier":{"issn":["1980-0436"]},"author":[{"id":"5c0e116e-803f-11ed-ab7e-90d572405f20","full_name":"Czudek, Klaudiusz S","last_name":"Czudek","first_name":"Klaudiusz S"},{"first_name":"Dmitry","full_name":"Dolgopyat, Dmitry","last_name":"Dolgopyat"}],"date_created":"2024-11-24T23:01:49Z","OA_type":"green","ec_funded":1,"date_published":"2024-11-01T00:00:00Z","external_id":{"arxiv":["2404.11700"],"isi":["001440992000003"]},"arxiv":1,"project":[{"name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020"}],"type":"journal_article","volume":21,"acknowledgement":"ents. The authors are grateful to Agnieszka Zelerowicz and the anonymous referee\r\nfor useful comments. The first author is grateful to Minsung Kim for providing some references.\r\nThe first author has been supported by the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 101034413. The second author has been supported by the NSF grant DMS 2246983.","isi":1,"title":"The central limit theorem and rate of mixing for simple random walks on the circle","_id":"18586","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","scopus_import":"1","article_processing_charge":"No","publication_status":"published","OA_place":"repository","department":[{"_id":"VaKa"}],"intvolume":"        21","publisher":"Instituto Nacional de Matematica Pura e Aplicada","oa":1,"month":"11","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2404.11700","open_access":"1"}],"day":"01","page":"1853-1865","article_type":"original","citation":{"chicago":"CZUDEK, Klaudiusz S, and Dmitry Dolgopyat. “The Central Limit Theorem and Rate of Mixing for Simple Random Walks on the Circle.” <i>Alea</i>. Instituto Nacional de Matematica Pura e Aplicada, 2024. <a href=\"https://doi.org/10.30757/ALEA.V21-70\">https://doi.org/10.30757/ALEA.V21-70</a>.","ama":"CZUDEK KS, Dolgopyat D. The central limit theorem and rate of mixing for simple random walks on the circle. <i>Alea</i>. 2024;21(2):1853-1865. doi:<a href=\"https://doi.org/10.30757/ALEA.V21-70\">10.30757/ALEA.V21-70</a>","ieee":"K. S. CZUDEK and D. Dolgopyat, “The central limit theorem and rate of mixing for simple random walks on the circle,” <i>Alea</i>, vol. 21, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1853–1865, 2024.","mla":"CZUDEK, Klaudiusz S., and Dmitry Dolgopyat. “The Central Limit Theorem and Rate of Mixing for Simple Random Walks on the Circle.” <i>Alea</i>, vol. 21, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2024, pp. 1853–65, doi:<a href=\"https://doi.org/10.30757/ALEA.V21-70\">10.30757/ALEA.V21-70</a>.","ista":"CZUDEK KS, Dolgopyat D. 2024. The central limit theorem and rate of mixing for simple random walks on the circle. Alea. 21(2), 1853–1865.","apa":"CZUDEK, K. S., &#38; Dolgopyat, D. (2024). The central limit theorem and rate of mixing for simple random walks on the circle. <i>Alea</i>. Instituto Nacional de Matematica Pura e Aplicada. <a href=\"https://doi.org/10.30757/ALEA.V21-70\">https://doi.org/10.30757/ALEA.V21-70</a>","short":"K.S. CZUDEK, D. Dolgopyat, Alea 21 (2024) 1853–1865."},"abstract":[{"text":"We prove the Central Limit Theorem and superpolynomial mixing for environment\r\nviewed from the particle process in quasi periodic Diophantine random environment. The main\r\ningredients are smoothness estimates for the solution of the Poisson equation and local limit asymptotics for certain accelerated walks.","lang":"eng"}]},{"isi":1,"type":"journal_article","volume":44,"_id":"17231","title":"Examples of projective billiards with open sets of periodic orbits","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","quality_controlled":"1","doi":"10.3934/dcds.2024059","oa_version":"Published Version","status":"public","issue":"11","language":[{"iso":"eng"}],"year":"2024","date_updated":"2026-06-18T17:54:16Z","author":[{"full_name":"Fiorebe, Corentin","last_name":"Fiorebe","id":"06619f18-9070-11eb-847d-d1ee780bd88b","first_name":"Corentin"}],"publication_identifier":{"issn":["1078-0947"],"eissn":["1553-5231"]},"publication":"Discrete and Continuous Dynamical Systems- Series A","date_created":"2024-07-14T22:01:10Z","date_published":"2024-11-01T00:00:00Z","OA_type":"free access","external_id":{"isi":["001230091000001"]},"oa":1,"month":"11","main_file_link":[{"url":"https://doi.org/10.3934/dcds.2024059","open_access":"1"}],"day":"01","page":"3287-3301","ddc":["500"],"article_type":"original","abstract":[{"text":"In the class of projective billiards, which contains the usual billiards, we exhibit counter-examples to Ivrii's conjecture, which states that in any planar billiard with smooth boundary the set of periodic orbits has zero measure. The counter-examples are polygons admitting a 2-parameters family of n-periodic orbits, with n being either 3 or any even integer greater than 4.","lang":"eng"}],"citation":{"ieee":"C. Fiorebe, “Examples of projective billiards with open sets of periodic orbits,” <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 44, no. 11. American Institute of Mathematical Sciences, pp. 3287–3301, 2024.","chicago":"Fiorebe, Corentin. “Examples of Projective Billiards with Open Sets of Periodic Orbits.” <i>Discrete and Continuous Dynamical Systems- Series A</i>. American Institute of Mathematical Sciences, 2024. <a href=\"https://doi.org/10.3934/dcds.2024059\">https://doi.org/10.3934/dcds.2024059</a>.","ama":"Fiorebe C. Examples of projective billiards with open sets of periodic orbits. <i>Discrete and Continuous Dynamical Systems- Series A</i>. 2024;44(11):3287-3301. doi:<a href=\"https://doi.org/10.3934/dcds.2024059\">10.3934/dcds.2024059</a>","mla":"Fiorebe, Corentin. “Examples of Projective Billiards with Open Sets of Periodic Orbits.” <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 44, no. 11, American Institute of Mathematical Sciences, 2024, pp. 3287–301, doi:<a href=\"https://doi.org/10.3934/dcds.2024059\">10.3934/dcds.2024059</a>.","short":"C. Fiorebe, Discrete and Continuous Dynamical Systems- Series A 44 (2024) 3287–3301.","ista":"Fiorebe C. 2024. Examples of projective billiards with open sets of periodic orbits. Discrete and Continuous Dynamical Systems- Series A. 44(11), 3287–3301.","apa":"Fiorebe, C. (2024). Examples of projective billiards with open sets of periodic orbits. <i>Discrete and Continuous Dynamical Systems- Series A</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/dcds.2024059\">https://doi.org/10.3934/dcds.2024059</a>"},"scopus_import":"1","article_processing_charge":"No","publication_status":"published","department":[{"_id":"VaKa"}],"intvolume":"        44","publisher":"American Institute of Mathematical Sciences"},{"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"MaKw"},{"_id":"VaKa"}],"publication_status":"published","file_date_updated":"2024-09-06T12:23:57Z","intvolume":"        75","publisher":"Oxford University Press","oa":1,"month":"06","day":"19","page":"869-899","article_type":"original","ddc":["500"],"citation":{"mla":"Koval, Illya, and Matthew Alan Kwan. “Exponentially Many Graphs Are Determined by Their Spectrum.” <i>Quarterly Journal of Mathematics</i>, vol. 75, no. 3, Oxford University Press, 2024, pp. 869–99, doi:<a href=\"https://doi.org/10.1093/qmath/haae030\">10.1093/qmath/haae030</a>.","ieee":"I. Koval and M. A. Kwan, “Exponentially many graphs are determined by their spectrum,” <i>Quarterly Journal of Mathematics</i>, vol. 75, no. 3. Oxford University Press, pp. 869–899, 2024.","ama":"Koval I, Kwan MA. Exponentially many graphs are determined by their spectrum. <i>Quarterly Journal of Mathematics</i>. 2024;75(3):869-899. doi:<a href=\"https://doi.org/10.1093/qmath/haae030\">10.1093/qmath/haae030</a>","chicago":"Koval, Illya, and Matthew Alan Kwan. “Exponentially Many Graphs Are Determined by Their Spectrum.” <i>Quarterly Journal of Mathematics</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/qmath/haae030\">https://doi.org/10.1093/qmath/haae030</a>.","apa":"Koval, I., &#38; Kwan, M. A. (2024). Exponentially many graphs are determined by their spectrum. <i>Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haae030\">https://doi.org/10.1093/qmath/haae030</a>","ista":"Koval I, Kwan MA. 2024. Exponentially many graphs are determined by their spectrum. Quarterly Journal of Mathematics. 75(3), 869–899.","short":"I. Koval, M.A. Kwan, Quarterly Journal of Mathematics 75 (2024) 869–899."},"abstract":[{"lang":"eng","text":"As a discrete analogue of Kac’s celebrated question on ‘hearing the shape of a drum’ and towards a practical\r\ngraph isomorphism test, it is of interest to understand which graphs are determined up to isomorphism by\r\ntheir spectrum (of their adjacency matrix). A striking conjecture in this area, due to van Dam and Haemers,\r\nis that ‘almost all graphs are determined by their spectrum’, meaning that the fraction of unlabelled n-vertex\r\ngraphs which are determined by their spectrum converges to 1 as n → ∞.\r\nIn this paper, we make a step towards this conjecture, showing that there are exponentially many n-vertex\r\ngraphs which are determined by their spectrum. This improves on previous bounds (of shape e\r\nc\r\n√\r\nn\r\n). We also\r\npropose a number of further directions of research.\r\n"}],"doi":"10.1093/qmath/haae030","oa_version":"Published Version","quality_controlled":"1","language":[{"iso":"eng"}],"issue":"3","status":"public","year":"2024","date_updated":"2025-09-08T09:09:41Z","publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"publication":"Quarterly Journal of Mathematics","author":[{"first_name":"Illya","full_name":"Koval, Illya","id":"2eed1f3b-896a-11ed-bdf8-93c7c4bf159e","last_name":"Koval"},{"first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan","last_name":"Kwan","orcid":"0000-0002-4003-7567"}],"date_created":"2024-09-01T22:01:07Z","file":[{"file_id":"17851","date_updated":"2024-09-06T12:23:57Z","content_type":"application/pdf","access_level":"open_access","checksum":"abf200d37ad69e6f2c0750a30296ad97","relation":"main_file","creator":"cchlebak","file_size":946411,"file_name":"2024_QuJofMath_Koval.pdf","success":1,"date_created":"2024-09-06T12:23:57Z"}],"date_published":"2024-06-19T00:00:00Z","external_id":{"isi":["001249741500001"],"arxiv":["2309.09788"]},"project":[{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","grant_number":"101076777","name":"Randomness and structure in combinatorics"}],"arxiv":1,"acknowledgement":"Matthew Kwan was supported by ERC Starting Grant ‘RANDSTRUCT’ No. 101076777.","volume":75,"type":"journal_article","isi":1,"title":"Exponentially many graphs are determined by their spectrum","_id":"17475","corr_author":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"has_accepted_license":"1"},{"publisher":"Elsevier","intvolume":"       457","file_date_updated":"2025-01-13T08:29:27Z","publication_status":"published","OA_place":"publisher","department":[{"_id":"VaKa"}],"article_processing_charge":"Yes (via OA deal)","scopus_import":"1","article_number":"109943","citation":{"mla":"Hou, Xuanji, et al. “Dynamical Classification of Analytic One-Frequency Quasi-Periodic SO(3,R)-Cocycles.” <i>Advances in Mathematics</i>, vol. 457, 109943, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.aim.2024.109943\">10.1016/j.aim.2024.109943</a>.","chicago":"Hou, Xuanji, Yi Pan, and Qi Zhou. “Dynamical Classification of Analytic One-Frequency Quasi-Periodic SO(3,R)-Cocycles.” <i>Advances in Mathematics</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.aim.2024.109943\">https://doi.org/10.1016/j.aim.2024.109943</a>.","ama":"Hou X, Pan Y, Zhou Q. Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles. <i>Advances in Mathematics</i>. 2024;457. doi:<a href=\"https://doi.org/10.1016/j.aim.2024.109943\">10.1016/j.aim.2024.109943</a>","ieee":"X. Hou, Y. Pan, and Q. Zhou, “Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles,” <i>Advances in Mathematics</i>, vol. 457. Elsevier, 2024.","short":"X. Hou, Y. Pan, Q. Zhou, Advances in Mathematics 457 (2024).","ista":"Hou X, Pan Y, Zhou Q. 2024. Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles. Advances in Mathematics. 457, 109943.","apa":"Hou, X., Pan, Y., &#38; Zhou, Q. (2024). Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2024.109943\">https://doi.org/10.1016/j.aim.2024.109943</a>"},"abstract":[{"text":"We establish a close connection between acceleration and dynamical degree for one-frequency quasi-periodic compact cocycles, by showing that two vectors derived separately from each coincide. Based on this, we provide a dynamical classification of one-frequency quasi-periodic  SO(3, R)-cocycles.","lang":"eng"}],"ddc":["510"],"article_type":"original","day":"01","month":"11","oa":1,"external_id":{"isi":["001315306500001"],"arxiv":["2311.17537"]},"date_published":"2024-11-01T00:00:00Z","ec_funded":1,"OA_type":"hybrid","date_created":"2024-09-15T22:01:39Z","file":[{"file_name":"2024_AdvancesMath_Hou.pdf","file_size":713659,"relation":"main_file","creator":"dernst","date_created":"2025-01-13T08:29:27Z","success":1,"access_level":"open_access","content_type":"application/pdf","date_updated":"2025-01-13T08:29:27Z","file_id":"18826","checksum":"1c80b844a91d93cf4799f4a65873b18d"}],"author":[{"last_name":"Hou","full_name":"Hou, Xuanji","first_name":"Xuanji"},{"first_name":"Yi","last_name":"Pan","id":"1e21c7f7-9070-11eb-847d-8b04c7169523","full_name":"Pan, Yi"},{"first_name":"Qi","full_name":"Zhou, Qi","last_name":"Zhou"}],"publication":"Advances in Mathematics","publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"year":"2024","date_updated":"2025-09-08T09:44:19Z","status":"public","language":[{"iso":"eng"}],"quality_controlled":"1","doi":"10.1016/j.aim.2024.109943","oa_version":"Published Version","has_accepted_license":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","_id":"18065","title":"Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles","isi":1,"volume":457,"acknowledgement":"X. Hou is partially supported by National Natural Science Foundation of China (Grant \r\n12071083) and Funds for Distinguished Youths of Hubei Province of China (\r\n2019CFA680). Y. Pan is supported by ERC Advanced Grant (#885707). Q. Zhou is partially supported by National Key R&D Program of China (2020YFA0713300), NSFC grant (\r\n12071232) and Nankai Zhide Foundation.","type":"journal_article","arxiv":1,"project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707","call_identifier":"H2020"}]},{"month":"08","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1905.00890","open_access":"1"}],"oa":1,"article_type":"original","citation":{"apa":"De Simoi, J., Kaloshin, V., &#38; Leguil, M. (2023). Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-023-01191-8\">https://doi.org/10.1007/s00222-023-01191-8</a>","ista":"De Simoi J, Kaloshin V, Leguil M. 2023. Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. Inventiones Mathematicae. 233, 829–901.","short":"J. De Simoi, V. Kaloshin, M. Leguil, Inventiones Mathematicae 233 (2023) 829–901.","chicago":"De Simoi, Jacopo, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectral Determination of Analytic Chaotic Billiards with Axial Symmetries.” <i>Inventiones Mathematicae</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00222-023-01191-8\">https://doi.org/10.1007/s00222-023-01191-8</a>.","ieee":"J. De Simoi, V. Kaloshin, and M. Leguil, “Marked Length Spectral determination of analytic chaotic billiards with axial symmetries,” <i>Inventiones Mathematicae</i>, vol. 233. Springer Nature, pp. 829–901, 2023.","ama":"De Simoi J, Kaloshin V, Leguil M. Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. <i>Inventiones Mathematicae</i>. 2023;233:829-901. doi:<a href=\"https://doi.org/10.1007/s00222-023-01191-8\">10.1007/s00222-023-01191-8</a>","mla":"De Simoi, Jacopo, et al. “Marked Length Spectral Determination of Analytic Chaotic Billiards with Axial Symmetries.” <i>Inventiones Mathematicae</i>, vol. 233, Springer Nature, 2023, pp. 829–901, doi:<a href=\"https://doi.org/10.1007/s00222-023-01191-8\">10.1007/s00222-023-01191-8</a>."},"abstract":[{"text":"We consider billiards obtained by removing from the plane finitely many strictly convex analytic obstacles satisfying the non-eclipse condition. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift, which provides a natural labeling of periodic orbits. We show that under suitable symmetry and genericity assumptions, the Marked Length Spectrum determines the geometry of the billiard table.","lang":"eng"}],"day":"01","page":"829-901","publication_status":"published","department":[{"_id":"VaKa"}],"scopus_import":"1","article_processing_charge":"No","intvolume":"       233","publisher":"Springer Nature","volume":233,"type":"journal_article","acknowledgement":"J.D.S. and M.L. have been partially supported by the NSERC Discovery grant, reference number 502617-2017. M.L. was also supported by the ERC project 692925 NUHGD of Sylvain Crovisier, by the ANR AAPG 2021 PRC CoSyDy: Conformally symplectic dynamics, beyond symplectic dynamics (ANR-CE40-0014), and by the ANR JCJC PADAWAN: Parabolic dynamics, bifurcations and wandering domains (ANR-21-CE40-0012). V.K. acknowledges partial support of the NSF grant DMS-1402164 and ERC Grant # 885707.","isi":1,"arxiv":1,"project":[{"_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707","name":"Spectral rigidity and integrability for billiards and geodesic flows","call_identifier":"H2020"}],"title":"Marked Length Spectral determination of analytic chaotic billiards with axial symmetries","_id":"12877","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2025-04-14T07:53:46Z","year":"2023","publication_identifier":{"issn":["0020-9910"],"eissn":["1432-1297"]},"publication":"Inventiones Mathematicae","author":[{"full_name":"De Simoi, Jacopo","first_name":"Jacopo","last_name":"De Simoi"},{"full_name":"Kaloshin, Vadim","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","orcid":"0000-0002-6051-2628"},{"first_name":"Martin","last_name":"Leguil","full_name":"Leguil, Martin"}],"doi":"10.1007/s00222-023-01191-8","oa_version":"Preprint","quality_controlled":"1","language":[{"iso":"eng"}],"status":"public","external_id":{"arxiv":["1905.00890"],"isi":["000978887600001"]},"date_created":"2023-04-30T22:01:05Z","ec_funded":1,"date_published":"2023-08-01T00:00:00Z"},{"project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","grant_number":"885707","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","call_identifier":"H2020"}],"arxiv":1,"isi":1,"type":"journal_article","acknowledgement":"VK acknowledges a partial support by the NSF grant DMS-1402164 and ERC Grant #885707. Discussions with Martin Leguil and Jacopo De Simoi were very useful. JC visited the University of Maryland and thanks for the hospitality. Also, JC was partially supported by the National Key Research and Development Program of China (No.2022YFA1005802), the NSFC Grant 12001392 and NSF of Jiangsu BK20200850. H.-K. Zhang is partially supported by the National Science Foundation (DMS-2220211), as well as Simons Foundation Collaboration Grants for Mathematicians (706383).","volume":404,"_id":"14427","title":"Length spectrum rigidity for piecewise analytic Bunimovich billiards","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","quality_controlled":"1","oa_version":"Preprint","doi":"10.1007/s00220-023-04837-z","status":"public","language":[{"iso":"eng"}],"date_updated":"2025-04-14T07:53:45Z","year":"2023","author":[{"full_name":"Chen, Jianyu","first_name":"Jianyu","last_name":"Chen"},{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628"},{"last_name":"Zhang","first_name":"Hong Kun","full_name":"Zhang, Hong Kun"}],"publication":"Communications in Mathematical Physics","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"date_created":"2023-10-15T22:01:11Z","date_published":"2023-11-01T00:00:00Z","ec_funded":1,"external_id":{"arxiv":["1902.07330"],"isi":["001073177200001"]},"oa":1,"month":"11","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.07330"}],"day":"01","page":"1-50","article_type":"original","abstract":[{"lang":"eng","text":"In the paper, we establish Squash Rigidity Theorem—the dynamical spectral rigidity for piecewise analytic Bunimovich squash-type stadia whose convex arcs are homothetic. We also establish Stadium Rigidity Theorem—the dynamical spectral rigidity for piecewise analytic Bunimovich stadia whose flat boundaries are a priori fixed. In addition, for smooth Bunimovich squash-type stadia we compute the Lyapunov exponents along the maximal period two orbit, as well as the value of the Peierls’ Barrier function from the maximal marked length spectrum associated to the rotation number 2n/4n+1."}],"citation":{"short":"J. Chen, V. Kaloshin, H.K. Zhang, Communications in Mathematical Physics 404 (2023) 1–50.","ista":"Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics. 404, 1–50.","apa":"Chen, J., Kaloshin, V., &#38; Zhang, H. K. (2023). Length spectrum rigidity for piecewise analytic Bunimovich billiards. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04837-z\">https://doi.org/10.1007/s00220-023-04837-z</a>","chicago":"Chen, Jianyu, Vadim Kaloshin, and Hong Kun Zhang. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04837-z\">https://doi.org/10.1007/s00220-023-04837-z</a>.","ama":"Chen J, Kaloshin V, Zhang HK. Length spectrum rigidity for piecewise analytic Bunimovich billiards. <i>Communications in Mathematical Physics</i>. 2023;404:1-50. doi:<a href=\"https://doi.org/10.1007/s00220-023-04837-z\">10.1007/s00220-023-04837-z</a>","ieee":"J. Chen, V. Kaloshin, and H. K. Zhang, “Length spectrum rigidity for piecewise analytic Bunimovich billiards,” <i>Communications in Mathematical Physics</i>, vol. 404. Springer Nature, pp. 1–50, 2023.","mla":"Chen, Jianyu, et al. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards.” <i>Communications in Mathematical Physics</i>, vol. 404, Springer Nature, 2023, pp. 1–50, doi:<a href=\"https://doi.org/10.1007/s00220-023-04837-z\">10.1007/s00220-023-04837-z</a>."},"scopus_import":"1","article_processing_charge":"No","department":[{"_id":"VaKa"}],"publication_status":"published","intvolume":"       404","publisher":"Springer Nature"},{"month":"07","type":"journal_article","acknowledgement":"The MFO and the workshop organizers would like to thank the National Science Foundation for supporting the participation of junior researchers in the workshop by the grant DMS-2230648, “US Junior Oberwolfach Fellows”.","volume":20,"article_type":"original","citation":{"chicago":"Arnaud, Marie-Claude, Michael Hutchings, and Vadim Kaloshin. “Dynamische Systeme.” <i>Oberwolfach Reports</i>. EMS Press, 2023. <a href=\"https://doi.org/10.4171/owr/2023/30\">https://doi.org/10.4171/owr/2023/30</a>.","ieee":"M.-C. Arnaud, M. Hutchings, and V. Kaloshin, “Dynamische Systeme,” <i>Oberwolfach Reports</i>, vol. 20, no. 3. EMS Press, pp. 1671–1730, 2023.","ama":"Arnaud M-C, Hutchings M, Kaloshin V. Dynamische Systeme. <i>Oberwolfach Reports</i>. 2023;20(3):1671-1730. doi:<a href=\"https://doi.org/10.4171/owr/2023/30\">10.4171/owr/2023/30</a>","mla":"Arnaud, Marie-Claude, et al. “Dynamische Systeme.” <i>Oberwolfach Reports</i>, vol. 20, no. 3, EMS Press, 2023, pp. 1671–730, doi:<a href=\"https://doi.org/10.4171/owr/2023/30\">10.4171/owr/2023/30</a>.","short":"M.-C. Arnaud, M. Hutchings, V. Kaloshin, Oberwolfach Reports 20 (2023) 1671–1730.","apa":"Arnaud, M.-C., Hutchings, M., &#38; Kaloshin, V. (2023). Dynamische Systeme. <i>Oberwolfach Reports</i>. EMS Press. <a href=\"https://doi.org/10.4171/owr/2023/30\">https://doi.org/10.4171/owr/2023/30</a>","ista":"Arnaud M-C, Hutchings M, Kaloshin V. 2023. Dynamische Systeme. Oberwolfach Reports. 20(3), 1671–1730."},"abstract":[{"lang":"eng","text":"This workshop continues a series of workshops whose current format originated in 1981 under then-organizers Moser and Zehnder, and whose latest iteration took place in July 2023. The general goal of this series of workshops is to discuss the latest developments in the field of dynamical systems, broadly construed, and its connections with neighboring areas of mathematics such as differential geometry, partial differential equations, and more recently contact and symplectic geometry. We continued this tradition, bringing in new participants working in areas of dynamical systems and its connections with other areas of mathematics that are currently highly active and/or showing great promise for future development. Key focus areas for the 2023 workshop include spectral rigidity for planar domains, chaotic and oscillatory motions in celestial mechanics, conformal symplectic dynamics, and relations between dynamics.he workshop by the grant DMS-2230648, “US Junior Oberwolfach Fellows”."}],"day":"09","_id":"18959","title":"Dynamische Systeme","page":"1671-1730","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","department":[{"_id":"VaKa"}],"date_updated":"2025-01-29T13:23:15Z","year":"2023","author":[{"last_name":"Arnaud","full_name":"Arnaud, Marie-Claude","first_name":"Marie-Claude"},{"last_name":"Hutchings","first_name":"Michael","full_name":"Hutchings, Michael"},{"last_name":"Kaloshin","first_name":"Vadim","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628"}],"publication_identifier":{"issn":["1660-8933"],"eissn":["1660-8941"]},"publication":"Oberwolfach Reports","quality_controlled":"1","oa_version":"None","doi":"10.4171/owr/2023/30","article_processing_charge":"No","issue":"3","status":"public","language":[{"iso":"eng"}],"intvolume":"        20","publisher":"EMS Press","date_created":"2025-01-29T13:19:15Z","date_published":"2023-07-09T00:00:00Z"},{"project":[{"call_identifier":"H2020","grant_number":"885707","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","name":"Spectral rigidity and integrability for billiards and geodesic flows"}],"type":"journal_article","acknowledgement":"We would also like to thank Dzmitry Dudko and Dierk Schleicher for many stimulating discussions and encouragement during our work on this project, and Weixiao Shen, Mikhail Hlushchanka and the referee for helpful comments. We are grateful to Leon Staresinic who carefully read the revised version of the manuscript and provided many helpful suggestions.","volume":8,"_id":"11553","title":"The dynamics of complex box mappings","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1007/s40598-022-00209-y"},{"url":"https://doi.org/10.1007/s40598-022-00218-x","relation":"erratum"}]},"has_accepted_license":"1","quality_controlled":"1","doi":"10.1007/s40598-022-00200-7","oa_version":"Published Version","status":"public","issue":"2","language":[{"iso":"eng"}],"date_updated":"2025-07-10T11:50:12Z","year":"2022","author":[{"last_name":"Clark","full_name":"Clark, Trevor","first_name":"Trevor"},{"id":"fe8209e2-906f-11eb-847d-950f8fc09115","full_name":"Drach, Kostiantyn","last_name":"Drach","first_name":"Kostiantyn","orcid":"0000-0002-9156-8616"},{"last_name":"Kozlovski","first_name":"Oleg","full_name":"Kozlovski, Oleg"},{"full_name":"Strien, Sebastian Van","first_name":"Sebastian Van","last_name":"Strien"}],"publication":"Arnold Mathematical Journal","publication_identifier":{"issn":["2199-6792"],"eissn":["2199-6806"]},"file":[{"access_level":"open_access","content_type":"application/pdf","date_updated":"2022-07-12T10:04:55Z","file_id":"11559","checksum":"16e7c659dee9073c6c8aeb87316ef201","file_size":2509915,"file_name":"2022_ArnoldMathematicalJournal_Clark.pdf","relation":"main_file","creator":"kschuh","date_created":"2022-07-12T10:04:55Z","success":1}],"date_created":"2022-07-10T22:01:53Z","date_published":"2022-06-01T00:00:00Z","OA_type":"hybrid","ec_funded":1,"oa":1,"month":"06","day":"01","page":"319-410","ddc":["500"],"article_type":"original","citation":{"ieee":"T. Clark, K. Drach, O. Kozlovski, and S. V. Strien, “The dynamics of complex box mappings,” <i>Arnold Mathematical Journal</i>, vol. 8, no. 2. Springer Nature, pp. 319–410, 2022.","ama":"Clark T, Drach K, Kozlovski O, Strien SV. The dynamics of complex box mappings. <i>Arnold Mathematical Journal</i>. 2022;8(2):319-410. doi:<a href=\"https://doi.org/10.1007/s40598-022-00200-7\">10.1007/s40598-022-00200-7</a>","chicago":"Clark, Trevor, Kostiantyn Drach, Oleg Kozlovski, and Sebastian Van Strien. “The Dynamics of Complex Box Mappings.” <i>Arnold Mathematical Journal</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40598-022-00200-7\">https://doi.org/10.1007/s40598-022-00200-7</a>.","mla":"Clark, Trevor, et al. “The Dynamics of Complex Box Mappings.” <i>Arnold Mathematical Journal</i>, vol. 8, no. 2, Springer Nature, 2022, pp. 319–410, doi:<a href=\"https://doi.org/10.1007/s40598-022-00200-7\">10.1007/s40598-022-00200-7</a>.","short":"T. Clark, K. Drach, O. Kozlovski, S.V. Strien, Arnold Mathematical Journal 8 (2022) 319–410.","apa":"Clark, T., Drach, K., Kozlovski, O., &#38; Strien, S. V. (2022). The dynamics of complex box mappings. <i>Arnold Mathematical Journal</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40598-022-00200-7\">https://doi.org/10.1007/s40598-022-00200-7</a>","ista":"Clark T, Drach K, Kozlovski O, Strien SV. 2022. The dynamics of complex box mappings. Arnold Mathematical Journal. 8(2), 319–410."},"abstract":[{"lang":"eng","text":"In holomorphic dynamics, complex box mappings arise as first return maps to wellchosen domains. They are a generalization of polynomial-like mapping, where the domain of the return map can have infinitely many components. They turned out to be extremely useful in tackling diverse problems. The purpose of this paper is:\r\n• To illustrate some pathologies that can occur when a complex box mapping is not induced by a globally defined map and when its domain has infinitely many components, and to give conditions to avoid these issues.\r\n• To show that once one has a box mapping for a rational map, these conditions can be assumed to hold in a very natural setting. Thus, we call such complex box mappings dynamically natural. Having such box mappings is the first step in tackling many problems in one-dimensional dynamics.\r\n• Many results in holomorphic dynamics rely on an interplay between combinatorial and analytic techniques. In this setting, some of these tools are:\r\n  • the Enhanced Nest (a nest of puzzle pieces around critical points) from Kozlovski, Shen, van Strien (AnnMath 165:749–841, 2007), referred to below as KSS;\r\n  • the Covering Lemma (which controls the moduli of pullbacks of annuli) from Kahn and Lyubich (Ann Math 169(2):561–593, 2009);\r\n   • the QC-Criterion and the Spreading Principle from KSS.\r\nThe purpose of this paper is to make these tools more accessible so that they can be used as a ‘black box’, so one does not have to redo the proofs in new settings.\r\n• To give an intuitive, but also rather detailed, outline of the proof from KSS and Kozlovski and van Strien (Proc Lond Math Soc (3) 99:275–296, 2009) of the following results for non-renormalizable dynamically natural complex box mappings:\r\n   • puzzle pieces shrink to points,\r\n   • (under some assumptions) topologically conjugate non-renormalizable polynomials and box mappings are quasiconformally conjugate.\r\n• We prove the fundamental ergodic properties for dynamically natural box mappings. This leads to some necessary conditions for when such a box mapping supports a measurable invariant line field on its filled Julia set. These mappings\r\nare the analogues of Lattès maps in this setting.\r\n• We prove a version of Mañé’s Theorem for complex box mappings concerning expansion along orbits of points that avoid a neighborhood of the set of critical points."}],"scopus_import":"1","article_processing_charge":"No","OA_place":"publisher","publication_status":"published","department":[{"_id":"VaKa"}],"file_date_updated":"2022-07-12T10:04:55Z","intvolume":"         8","publisher":"Springer Nature"},{"isi":1,"type":"journal_article","acknowledgement":"We are grateful to a number of colleagues for helpful and inspiring discussions during the time when we worked on this project, in particular Dima Dudko, Misha Hlushchanka, John Hubbard, Misha Lyubich, Oleg Kozlovski, and Sebastian van Strien. Finally, we would like to thank our dynamics research group for numerous helpful and enjoyable discussions: Konstantin Bogdanov, Roman Chernov, Russell Lodge, Steffen Maaß, David Pfrang, Bernhard Reinke, Sergey Shemyakov, and Maik Sowinski. We gratefully acknowledge support by the Advanced Grant “HOLOGRAM” (#695 621) of the European Research Council (ERC), as well as hospitality of Cornell University in the spring of 2018 while much of this work was prepared. The first-named author also acknowledges the support of the ERC Advanced Grant “SPERIG” (#885 707).","volume":408,"project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","grant_number":"885707","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","call_identifier":"H2020"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"has_accepted_license":"1","_id":"11717","title":"Rigidity of Newton dynamics","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","corr_author":"1","year":"2022","date_updated":"2025-04-14T07:53:45Z","author":[{"orcid":"0000-0002-9156-8616","full_name":"Drach, Kostiantyn","id":"fe8209e2-906f-11eb-847d-950f8fc09115","first_name":"Kostiantyn","last_name":"Drach"},{"full_name":"Schleicher, Dierk","first_name":"Dierk","last_name":"Schleicher"}],"publication":"Advances in Mathematics","publication_identifier":{"issn":["0001-8708"]},"quality_controlled":"1","oa_version":"Published Version","doi":"10.1016/j.aim.2022.108591","issue":"Part A","status":"public","language":[{"iso":"eng"}],"external_id":{"isi":["000860924200005"]},"file":[{"file_id":"12474","date_updated":"2023-02-02T07:39:09Z","content_type":"application/pdf","access_level":"open_access","checksum":"2710e6f5820f8c20a676ddcbb30f0e8d","creator":"dernst","relation":"main_file","file_name":"2022_AdvancesMathematics_Drach.pdf","file_size":2164036,"success":1,"date_created":"2023-02-02T07:39:09Z"}],"date_created":"2022-08-01T17:08:16Z","date_published":"2022-10-29T00:00:00Z","ec_funded":1,"month":"10","oa":1,"ddc":["510"],"article_type":"original","abstract":[{"lang":"eng","text":"We study rigidity of rational maps that come from Newton's root finding method for polynomials of arbitrary degrees. We establish dynamical rigidity of these maps: each point in the Julia set of a Newton map is either rigid (i.e. its orbit can be distinguished in combinatorial terms from all other orbits), or the orbit of this point eventually lands in the filled-in Julia set of a polynomial-like restriction of the original map. As a corollary, we show that the Julia sets of Newton maps in many non-trivial cases are locally connected; in particular, every cubic Newton map without Siegel points has locally connected Julia set.\r\nIn the parameter space of Newton maps of arbitrary degree we obtain the following rigidity result: any two combinatorially equivalent Newton maps are quasiconformally conjugate in a neighborhood of their Julia sets provided that they either non-renormalizable, or they are both renormalizable “in the same way”.\r\nOur main tool is a generalized renormalization concept called “complex box mappings” for which we extend a dynamical rigidity result by Kozlovski and van Strien so as to include irrationally indifferent and renormalizable situations."}],"citation":{"short":"K. Drach, D. Schleicher, Advances in Mathematics 408 (2022).","ista":"Drach K, Schleicher D. 2022. Rigidity of Newton dynamics. Advances in Mathematics. 408(Part A), 108591.","apa":"Drach, K., &#38; Schleicher, D. (2022). Rigidity of Newton dynamics. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2022.108591\">https://doi.org/10.1016/j.aim.2022.108591</a>","ieee":"K. Drach and D. Schleicher, “Rigidity of Newton dynamics,” <i>Advances in Mathematics</i>, vol. 408, no. Part A. Elsevier, 2022.","chicago":"Drach, Kostiantyn, and Dierk Schleicher. “Rigidity of Newton Dynamics.” <i>Advances in Mathematics</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.aim.2022.108591\">https://doi.org/10.1016/j.aim.2022.108591</a>.","ama":"Drach K, Schleicher D. Rigidity of Newton dynamics. <i>Advances in Mathematics</i>. 2022;408(Part A). doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108591\">10.1016/j.aim.2022.108591</a>","mla":"Drach, Kostiantyn, and Dierk Schleicher. “Rigidity of Newton Dynamics.” <i>Advances in Mathematics</i>, vol. 408, no. Part A, 108591, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108591\">10.1016/j.aim.2022.108591</a>."},"day":"29","department":[{"_id":"VaKa"}],"publication_status":"published","file_date_updated":"2023-02-02T07:39:09Z","scopus_import":"1","article_number":"108591","article_processing_charge":"Yes (via OA deal)","intvolume":"       408","publisher":"Elsevier","keyword":["General Mathematics"]},{"external_id":{"isi":["000865267300002"],"arxiv":["2105.14640"]},"date_created":"2023-01-12T12:06:49Z","ec_funded":1,"date_published":"2022-10-03T00:00:00Z","date_updated":"2025-04-14T07:53:45Z","year":"2022","publication_identifier":{"eissn":["1468-4845"],"issn":["1560-3547"]},"publication":"Regular and Chaotic Dynamics","author":[{"orcid":"0000-0003-2640-4049","first_name":"Edmond","last_name":"Koudjinan","full_name":"Koudjinan, Edmond","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E"},{"orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim"}],"doi":"10.1134/S1560354722050021","oa_version":"Preprint","quality_controlled":"1","language":[{"iso":"eng"}],"issue":"6","status":"public","related_material":{"link":[{"url":"https://doi.org/10.1134/s1560354722060107","relation":"erratum"}]},"title":"On some invariants of Birkhoff billiards under conjugacy","_id":"12145","corr_author":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","volume":27,"acknowledgement":"We are grateful to the anonymous referees for their careful reading and valuable remarks and\r\ncomments which helped to improve the paper significantly. We gratefully acknowledge support from the European Research Council (ERC) through the Advanced Grant “SPERIG” (#885707).","type":"journal_article","isi":1,"project":[{"grant_number":"885707","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","name":"Spectral rigidity and integrability for billiards and geodesic flows","call_identifier":"H2020"}],"arxiv":1,"intvolume":"        27","publisher":"Springer Nature","keyword":["Mechanical Engineering","Applied Mathematics","Mathematical Physics","Modeling and Simulation","Statistical and Nonlinear Physics","Mathematics (miscellaneous)"],"publication_status":"published","department":[{"_id":"VaKa"}],"scopus_import":"1","article_processing_charge":"No","article_type":"original","citation":{"mla":"Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards under Conjugacy.” <i>Regular and Chaotic Dynamics</i>, vol. 27, no. 6, Springer Nature, 2022, pp. 525–37, doi:<a href=\"https://doi.org/10.1134/S1560354722050021\">10.1134/S1560354722050021</a>.","ama":"Koudjinan E, Kaloshin V. On some invariants of Birkhoff billiards under conjugacy. <i>Regular and Chaotic Dynamics</i>. 2022;27(6):525-537. doi:<a href=\"https://doi.org/10.1134/S1560354722050021\">10.1134/S1560354722050021</a>","chicago":"Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards under Conjugacy.” <i>Regular and Chaotic Dynamics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1134/S1560354722050021\">https://doi.org/10.1134/S1560354722050021</a>.","ieee":"E. Koudjinan and V. Kaloshin, “On some invariants of Birkhoff billiards under conjugacy,” <i>Regular and Chaotic Dynamics</i>, vol. 27, no. 6. Springer Nature, pp. 525–537, 2022.","short":"E. Koudjinan, V. Kaloshin, Regular and Chaotic Dynamics 27 (2022) 525–537.","apa":"Koudjinan, E., &#38; Kaloshin, V. (2022). On some invariants of Birkhoff billiards under conjugacy. <i>Regular and Chaotic Dynamics</i>. Springer Nature. <a href=\"https://doi.org/10.1134/S1560354722050021\">https://doi.org/10.1134/S1560354722050021</a>","ista":"Koudjinan E, Kaloshin V. 2022. On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. 27(6), 525–537."},"abstract":[{"lang":"eng","text":"In the class of strictly convex smooth boundaries each of which has no strip around its boundary foliated by invariant curves, we prove that the Taylor coefficients of the “normalized” Mather’s β-function are invariant under C∞-conjugacies. In contrast, we prove that any two elliptic billiard maps are C0-conjugate near their respective boundaries, and C∞-conjugate, near the boundary and away from a line passing through the center of the underlying ellipse. We also prove that, if the billiard maps corresponding to two ellipses are topologically conjugate, then the two ellipses are similar."}],"day":"03","page":"525-537","month":"10","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.14640","open_access":"1"}],"oa":1},{"publication_status":"published","department":[{"_id":"VaKa"}],"article_processing_charge":"No","scopus_import":"1","publisher":"Springer Nature","intvolume":"         8","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2110.10750"}],"month":"10","oa":1,"citation":{"ieee":"M. Bialy, C. Fiorebe, A. Glutsyuk, M. Levi, A. Plakhov, and S. Tabachnikov, “Open problems on billiards and geometric optics,” <i>Arnold Mathematical Journal</i>, vol. 8. Springer Nature, pp. 411–422, 2022.","ama":"Bialy M, Fiorebe C, Glutsyuk A, Levi M, Plakhov A, Tabachnikov S. Open problems on billiards and geometric optics. <i>Arnold Mathematical Journal</i>. 2022;8:411-422. doi:<a href=\"https://doi.org/10.1007/s40598-022-00198-y\">10.1007/s40598-022-00198-y</a>","chicago":"Bialy, Misha, Corentin Fiorebe, Alexey Glutsyuk, Mark Levi, Alexander Plakhov, and Serge Tabachnikov. “Open Problems on Billiards and Geometric Optics.” <i>Arnold Mathematical Journal</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40598-022-00198-y\">https://doi.org/10.1007/s40598-022-00198-y</a>.","mla":"Bialy, Misha, et al. “Open Problems on Billiards and Geometric Optics.” <i>Arnold Mathematical Journal</i>, vol. 8, Springer Nature, 2022, pp. 411–22, doi:<a href=\"https://doi.org/10.1007/s40598-022-00198-y\">10.1007/s40598-022-00198-y</a>.","ista":"Bialy M, Fiorebe C, Glutsyuk A, Levi M, Plakhov A, Tabachnikov S. 2022. Open problems on billiards and geometric optics. Arnold Mathematical Journal. 8, 411–422.","apa":"Bialy, M., Fiorebe, C., Glutsyuk, A., Levi, M., Plakhov, A., &#38; Tabachnikov, S. (2022). Open problems on billiards and geometric optics. <i>Arnold Mathematical Journal</i>. Hybrid: Springer Nature. <a href=\"https://doi.org/10.1007/s40598-022-00198-y\">https://doi.org/10.1007/s40598-022-00198-y</a>","short":"M. Bialy, C. Fiorebe, A. Glutsyuk, M. Levi, A. Plakhov, S. Tabachnikov, Arnold Mathematical Journal 8 (2022) 411–422."},"abstract":[{"lang":"eng","text":"This is a collection of problems composed by some participants of the workshop “Differential Geometry, Billiards, and Geometric Optics” that took place at CIRM on October 4–8, 2021."}],"article_type":"original","page":"411-422","day":"01","publication":"Arnold Mathematical Journal","publication_identifier":{"eissn":["2199-6806"],"issn":["2199-6792"]},"author":[{"first_name":"Misha","last_name":"Bialy","full_name":"Bialy, Misha"},{"id":"06619f18-9070-11eb-847d-d1ee780bd88b","last_name":"Fiorebe","full_name":"Fiorebe, Corentin","first_name":"Corentin"},{"full_name":"Glutsyuk, Alexey","first_name":"Alexey","last_name":"Glutsyuk"},{"last_name":"Levi","first_name":"Mark","full_name":"Levi, Mark"},{"last_name":"Plakhov","full_name":"Plakhov, Alexander","first_name":"Alexander"},{"full_name":"Tabachnikov, Serge","first_name":"Serge","last_name":"Tabachnikov"}],"year":"2022","date_updated":"2023-02-27T07:34:08Z","conference":{"location":"Hybrid","start_date":"2021-10-04","name":"CIRM: Centre International de Rencontres Mathématiques","end_date":"2021-10-08"},"language":[{"iso":"eng"}],"status":"public","oa_version":"Preprint","doi":"10.1007/s40598-022-00198-y","quality_controlled":"1","external_id":{"arxiv":["2110.10750"]},"date_published":"2022-10-01T00:00:00Z","date_created":"2022-01-30T23:01:34Z","type":"journal_article","volume":8,"arxiv":1,"related_material":{"link":[{"relation":"earlier_version","url":"https://conferences.cirm-math.fr/2383.html"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Open problems on billiards and geometric optics","_id":"10706"},{"article_processing_charge":"No","scopus_import":"1","department":[{"_id":"VaKa"}],"publication_status":"published","das_tickbox":"1","publisher":"EMS Press","intvolume":"        18","oa":1,"main_file_link":[{"url":"https://www.doi.org/10.4171/OWR/2021/33","open_access":"1"}],"month":"11","page":"1735-1803","day":"26","abstract":[{"text":"This workshop continued a biannual series of workshops at Oberwolfach on dynamical systems that started with a meeting organized by Moser and Zehnder in 1981. Workshops in this series focus on new results and developments in dynamical systems and related areas of mathematics, with symplectic geometry playing an important role in recent years in connection with Hamiltonian dynamics. In this year special emphasis was placed on various kinds of spectra (in contact geometry, in Riemannian geometry, in dynamical systems and in symplectic topology) and their applications to dynamics.","lang":"eng"}],"citation":{"chicago":"Arnaud, Marie-Claude, Helmut W. Hofer, Michael Hutchings, and Vadim Kaloshin. “Dynamische Systeme.” <i>Oberwolfach Reports</i>. EMS Press, 2022. <a href=\"https://doi.org/10.4171/owr/2021/33\">https://doi.org/10.4171/owr/2021/33</a>.","ieee":"M.-C. Arnaud, H. W. Hofer, M. Hutchings, and V. Kaloshin, “Dynamische Systeme,” <i>Oberwolfach Reports</i>, vol. 18, no. 3. EMS Press, pp. 1735–1803, 2022.","ama":"Arnaud M-C, Hofer HW, Hutchings M, Kaloshin V. Dynamische Systeme. <i>Oberwolfach Reports</i>. 2022;18(3):1735-1803. doi:<a href=\"https://doi.org/10.4171/owr/2021/33\">10.4171/owr/2021/33</a>","mla":"Arnaud, Marie-Claude, et al. “Dynamische Systeme.” <i>Oberwolfach Reports</i>, vol. 18, no. 3, EMS Press, 2022, pp. 1735–803, doi:<a href=\"https://doi.org/10.4171/owr/2021/33\">10.4171/owr/2021/33</a>.","ista":"Arnaud M-C, Hofer HW, Hutchings M, Kaloshin V. 2022. Dynamische Systeme. Oberwolfach Reports. 18(3), 1735–1803.","apa":"Arnaud, M.-C., Hofer, H. W., Hutchings, M., &#38; Kaloshin, V. (2022). Dynamische Systeme. <i>Oberwolfach Reports</i>. EMS Press. <a href=\"https://doi.org/10.4171/owr/2021/33\">https://doi.org/10.4171/owr/2021/33</a>","short":"M.-C. Arnaud, H.W. Hofer, M. Hutchings, V. Kaloshin, Oberwolfach Reports 18 (2022) 1735–1803."},"ddc":["500"],"article_type":"original","issue":"3","status":"public","language":[{"iso":"eng"}],"quality_controlled":"1","oa_version":"Published Version","doi":"10.4171/owr/2021/33","author":[{"full_name":"Arnaud, Marie-Claude","last_name":"Arnaud","first_name":"Marie-Claude"},{"full_name":"Hofer, Helmut W.","last_name":"Hofer","first_name":"Helmut W."},{"first_name":"Michael","full_name":"Hutchings, Michael","last_name":"Hutchings"},{"first_name":"Vadim","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628"}],"publication":"Oberwolfach Reports","publication_identifier":{"eissn":["1660-8941"],"issn":["1660-8933"]},"date_updated":"2026-07-06T11:52:32Z","year":"2022","date_published":"2022-11-26T00:00:00Z","date_created":"2024-05-29T06:01:19Z","type":"journal_article","volume":18,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","_id":"17063","title":"Dynamische Systeme"}]