[{"status":"public","scopus_import":"1","license":"https://creativecommons.org/licenses/by/4.0/","ec_funded":1,"publication":"Inventiones Mathematicae","date_updated":"2025-12-29T11:37:48Z","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2025","main_file_link":[{"url":"https://doi.org/10.1007/s00222-025-01397-y","open_access":"1"}],"OA_place":"publisher","date_published":"2025-12-11T00:00:00Z","quality_controlled":"1","type":"journal_article","external_id":{"arxiv":["2111.12171"]},"_id":"14278","language":[{"iso":"eng"}],"abstract":[{"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.","lang":"eng"}],"day":"11","citation":{"ieee":"I. Koval, “Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse,” <i>Inventiones Mathematicae</i>. Springer Nature, 2025.","short":"I. Koval, Inventiones Mathematicae (2025).","mla":"Koval, Illya. “Local Strong Birkhoff Conjecture and Local Spectral Rigidity of Almost Every Ellipse.” <i>Inventiones Mathematicae</i>, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00222-025-01397-y\">10.1007/s00222-025-01397-y</a>.","apa":"Koval, I. (2025). 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>","ista":"Koval I. 2025. Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse. Inventiones Mathematicae.","ama":"Koval I. Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse. <i>Inventiones Mathematicae</i>. 2025. 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, 2025. <a href=\"https://doi.org/10.1007/s00222-025-01397-y\">https://doi.org/10.1007/s00222-025-01397-y</a>."},"has_accepted_license":"1","publisher":"Springer Nature","article_processing_charge":"Yes (via OA deal)","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"corr_author":"1","doi":"10.1007/s00222-025-01397-y","oa":1,"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).","month":"12","department":[{"_id":"GradSch"},{"_id":"VaKa"}],"article_type":"original","project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","call_identifier":"H2020","grant_number":"885707"}],"author":[{"full_name":"Koval, Illya","last_name":"Koval","id":"2eed1f3b-896a-11ed-bdf8-93c7c4bf159e","first_name":"Illya"}],"publication_identifier":{"issn":["0020-9910"],"eissn":["1432-1297"]},"arxiv":1,"OA_type":"hybrid","oa_version":"Published Version","title":"Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse","date_created":"2023-09-06T08:35:43Z","publication_status":"epub_ahead"},{"date_created":"2025-08-17T22:01:35Z","title":"Local rigidity for symplectic billiards","OA_type":"hybrid","oa_version":"Published Version","arxiv":1,"publication_identifier":{"issn":["1050-6926"]},"file":[{"access_level":"open_access","success":1,"content_type":"application/pdf","date_created":"2025-12-30T09:28:58Z","file_size":484344,"checksum":"ed86500742b3fd93db3287558a630383","file_name":"2025_JourGeomAnalysis_Tsodikovich.pdf","creator":"dernst","file_id":"20907","relation":"main_file","date_updated":"2025-12-30T09:28:58Z"}],"publication_status":"published","article_processing_charge":"Yes (via OA deal)","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"corr_author":"1","publisher":"Springer Nature","author":[{"id":"04531810-fb3e-11ef-87f0-800a4ce333db","first_name":"Daniel","last_name":"Tsodikovich","full_name":"Tsodikovich, Daniel"}],"volume":35,"month":"08","department":[{"_id":"VaKa"}],"project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707"}],"article_type":"original","doi":"10.1007/s12220-025-02148-4","oa":1,"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","OA_place":"publisher","date_published":"2025-08-07T00:00:00Z","intvolume":"        35","article_number":"306","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["510"],"year":"2025","day":"07","citation":{"ieee":"D. Tsodikovich, “Local rigidity for symplectic billiards,” <i>Journal of Geometric Analysis</i>, vol. 35, no. 10. Springer Nature, 2025.","short":"D. Tsodikovich, Journal of Geometric Analysis 35 (2025).","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>.","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>","ista":"Tsodikovich D. 2025. Local rigidity for symplectic billiards. Journal of Geometric Analysis. 35(10), 306.","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>."},"has_accepted_license":"1","external_id":{"arxiv":["2501.08849"],"isi":["001546433200002"]},"language":[{"iso":"eng"}],"_id":"20185","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."}],"quality_controlled":"1","type":"journal_article","ec_funded":1,"issue":"10","scopus_import":"1","PlanS_conform":"1","status":"public","date_updated":"2025-12-30T09:29:27Z","publication":"Journal of Geometric Analysis","isi":1,"file_date_updated":"2025-12-30T09:28:58Z"},{"publisher":"Cambridge University Press","article_processing_charge":"Yes (via OA deal)","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"corr_author":"1","related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"}]},"doi":"10.1017/etds.2024.48","oa":1,"acknowledgement":"I am very grateful to Vadim Kaloshin for suggesting the topic, his guidance during this project, and many helpful comments on an earlier version of the manuscript. Moreover, I would like to thank Comlan Edmond Koudjinan and Volodymyr Riabov for interesting discussions. Partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331 is gratefully acknowledged. This project received funding from the European Research Council (ERC) ERC Grant No. 885707.","department":[{"_id":"LaEr"}],"month":"02","article_type":"original","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"},{"name":"Spectral rigidity and integrability for billiards and geodesic flows","grant_number":"885707","call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A"}],"volume":45,"author":[{"full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"}],"publication_identifier":{"eissn":["1469-4417"],"issn":["0143-3857"]},"OA_type":"hybrid","oa_version":"Published Version","date_created":"2024-09-22T22:01:43Z","title":"Deformational rigidity of integrable metrics on the torus","publication_status":"published","file":[{"access_level":"open_access","content_type":"application/pdf","success":1,"date_created":"2025-01-13T08:51:40Z","file_size":659100,"checksum":"650fe115d998fe0ac3a8d0c7519447c8","file_name":"2025_ErgodicTheory_Henheik.pdf","file_id":"18828","date_updated":"2025-01-13T08:51:40Z","creator":"dernst","relation":"main_file"}],"page":"467-503","status":"public","scopus_import":"1","ec_funded":1,"issue":"2","file_date_updated":"2025-01-13T08:51:40Z","isi":1,"date_updated":"2026-04-07T12:37:10Z","publication":"Ergodic Theory and Dynamical Systems","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2025","intvolume":"        45","OA_place":"publisher","date_published":"2025-02-01T00:00:00Z","quality_controlled":"1","type":"journal_article","external_id":{"isi":["001308182000001"]},"language":[{"iso":"eng"}],"_id":"18112","abstract":[{"text":"It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville metrics. In this paper, we study a deformative version of this conjecture: we consider integrable deformations of a non-flat Liouville metric in a conformal class and show that for a fairly large class of such deformations, the deformed metric is again Liouville. The principal idea of the argument is that the preservation of rational invariant tori in the foliation of the phase space forces a linear combination on the Fourier coefficients of the deformation to vanish. Showing that the resulting linear system is non-degenerate will then yield the claim. Since our method of proof immediately carries over to higher dimensional tori, we obtain analogous statements in this more general case. To put our results in perspective, we review existing results about integrable metrics on the torus.","lang":"eng"}],"citation":{"chicago":"Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on the Torus.” <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/etds.2024.48\">https://doi.org/10.1017/etds.2024.48</a>.","ama":"Henheik SJ. Deformational rigidity of integrable metrics on the torus. <i>Ergodic Theory and Dynamical Systems</i>. 2025;45(2):467-503. doi:<a href=\"https://doi.org/10.1017/etds.2024.48\">10.1017/etds.2024.48</a>","ista":"Henheik SJ. 2025. Deformational rigidity of integrable metrics on the torus. Ergodic Theory and Dynamical Systems. 45(2), 467–503.","apa":"Henheik, S. J. (2025). Deformational rigidity of integrable metrics on the torus. <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/etds.2024.48\">https://doi.org/10.1017/etds.2024.48</a>","mla":"Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on the Torus.” <i>Ergodic Theory and Dynamical Systems</i>, vol. 45, no. 2, Cambridge University Press, 2025, pp. 467–503, doi:<a href=\"https://doi.org/10.1017/etds.2024.48\">10.1017/etds.2024.48</a>.","short":"S.J. Henheik, Ergodic Theory and Dynamical Systems 45 (2025) 467–503.","ieee":"S. J. Henheik, “Deformational rigidity of integrable metrics on the torus,” <i>Ergodic Theory and Dynamical Systems</i>, vol. 45, no. 2. Cambridge University Press, pp. 467–503, 2025."},"day":"01","has_accepted_license":"1"},{"publication_identifier":{"issn":["0001-8708"],"eissn":["1090-2082"]},"arxiv":1,"date_created":"2024-09-15T22:01:39Z","title":"Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles","oa_version":"Published Version","OA_type":"hybrid","publication_status":"published","file":[{"access_level":"open_access","date_created":"2025-01-13T08:29:27Z","file_size":713659,"content_type":"application/pdf","success":1,"file_name":"2024_AdvancesMath_Hou.pdf","checksum":"1c80b844a91d93cf4799f4a65873b18d","date_updated":"2025-01-13T08:29:27Z","file_id":"18826","relation":"main_file","creator":"dernst"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"corr_author":"1","article_processing_charge":"Yes (via OA deal)","publisher":"Elsevier","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.","oa":1,"doi":"10.1016/j.aim.2024.109943","author":[{"last_name":"Hou","full_name":"Hou, Xuanji","first_name":"Xuanji"},{"last_name":"Pan","full_name":"Pan, Yi","first_name":"Yi","id":"1e21c7f7-9070-11eb-847d-8b04c7169523"},{"full_name":"Zhou, Qi","last_name":"Zhou","first_name":"Qi"}],"volume":457,"project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","call_identifier":"H2020","grant_number":"885707"}],"article_type":"original","department":[{"_id":"VaKa"}],"month":"11","article_number":"109943","intvolume":"       457","year":"2024","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","ddc":["510"],"date_published":"2024-11-01T00:00:00Z","OA_place":"publisher","_id":"18065","language":[{"iso":"eng"}],"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"}],"external_id":{"isi":["001315306500001"],"arxiv":["2311.17537"]},"type":"journal_article","quality_controlled":"1","has_accepted_license":"1","day":"01","citation":{"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>","short":"X. Hou, Y. Pan, Q. Zhou, Advances in Mathematics 457 (2024).","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.","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>.","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.","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>"},"status":"public","ec_funded":1,"scopus_import":"1","file_date_updated":"2025-01-13T08:29:27Z","date_updated":"2025-09-08T09:44:19Z","publication":"Advances in Mathematics","isi":1},{"year":"2024","ddc":["510"],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","intvolume":"        34","date_published":"2024-12-01T00:00:00Z","OA_place":"publisher","type":"journal_article","quality_controlled":"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"}],"_id":"18483","language":[{"iso":"eng"}],"external_id":{"isi":["001329804200001"],"arxiv":["2306.12301"]},"has_accepted_license":"1","day":"01","citation":{"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>","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>","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>.","short":"V. Kaloshin, E. Koudjinan, K. Zhang, Geometric and Functional Analysis 34 (2024) 1973–2007.","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."},"status":"public","page":"1973-2007","scopus_import":"1","ec_funded":1,"file_date_updated":"2025-01-13T09:14:24Z","isi":1,"publication":"Geometric and Functional Analysis","date_updated":"2025-09-08T14:27:45Z","publication_identifier":{"issn":["1016-443X"],"eissn":["1420-8970"]},"arxiv":1,"oa_version":"Published Version","OA_type":"hybrid","title":"Birkhoff conjecture for nearly centrally symmetric domains","date_created":"2024-10-27T23:01:45Z","publication_status":"published","file":[{"relation":"main_file","creator":"dernst","date_updated":"2025-01-13T09:14:24Z","file_id":"18833","file_name":"2024_GeometricFunctionalAnalysis_Kaloshin.pdf","checksum":"e7fcd9f78beb40408c7d858ac0625e27","file_size":2260980,"date_created":"2025-01-13T09:14:24Z","success":1,"content_type":"application/pdf","access_level":"open_access"}],"publisher":"Springer Nature","corr_author":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_processing_charge":"Yes (via OA deal)","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).","doi":"10.1007/s00039-024-00695-6","oa":1,"article_type":"original","project":[{"_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","call_identifier":"H2020","grant_number":"885707","name":"Spectral rigidity and integrability for billiards and geodesic flows"}],"month":"12","department":[{"_id":"VaKa"}],"volume":34,"author":[{"orcid":"0000-0002-6051-2628","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","last_name":"Kaloshin"},{"orcid":"0000-0003-2640-4049","first_name":"Edmond","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","last_name":"Koudjinan","full_name":"Koudjinan, Edmond"},{"last_name":"Zhang","full_name":"Zhang, Ke","first_name":"Ke"}]},{"publisher":"Springer Nature","corr_author":"1","article_processing_charge":"No","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).","oa":1,"doi":"10.1007/s00220-023-04837-z","project":[{"grant_number":"885707","call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","name":"Spectral rigidity and integrability for billiards and geodesic flows"}],"article_type":"original","department":[{"_id":"VaKa"}],"month":"11","author":[{"first_name":"Jianyu","last_name":"Chen","full_name":"Chen, Jianyu"},{"first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","full_name":"Kaloshin, Vadim"},{"first_name":"Hong Kun","full_name":"Zhang, Hong Kun","last_name":"Zhang"}],"volume":404,"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"arxiv":1,"oa_version":"Preprint","date_created":"2023-10-15T22:01:11Z","title":"Length spectrum rigidity for piecewise analytic Bunimovich billiards","publication_status":"published","page":"1-50","status":"public","scopus_import":"1","ec_funded":1,"isi":1,"publication":"Communications in Mathematical Physics","date_updated":"2025-04-14T07:53:45Z","year":"2023","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"       404","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.07330"}],"date_published":"2023-11-01T00:00:00Z","type":"journal_article","quality_controlled":"1","language":[{"iso":"eng"}],"_id":"14427","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."}],"external_id":{"isi":["001073177200001"],"arxiv":["1902.07330"]},"day":"01","citation":{"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.","short":"J. Chen, V. Kaloshin, H.K. Zhang, Communications in Mathematical Physics 404 (2023) 1–50.","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>.","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>","ista":"Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics. 404, 1–50.","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>","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>."}},{"scopus_import":"1","ec_funded":1,"status":"public","page":"829-901","isi":1,"date_updated":"2025-04-14T07:53:46Z","publication":"Inventiones Mathematicae","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1905.00890","open_access":"1"}],"date_published":"2023-08-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2023","intvolume":"       233","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>","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>.","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.","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>.","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>","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."},"day":"01","quality_controlled":"1","type":"journal_article","external_id":{"isi":["000978887600001"],"arxiv":["1905.00890"]},"language":[{"iso":"eng"}],"_id":"12877","abstract":[{"lang":"eng","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."}],"publisher":"Springer Nature","article_processing_charge":"No","department":[{"_id":"VaKa"}],"month":"08","article_type":"original","project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","grant_number":"885707","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","call_identifier":"H2020"}],"volume":233,"author":[{"full_name":"De Simoi, Jacopo","last_name":"De Simoi","first_name":"Jacopo"},{"first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","last_name":"Kaloshin"},{"last_name":"Leguil","full_name":"Leguil, Martin","first_name":"Martin"}],"doi":"10.1007/s00222-023-01191-8","oa":1,"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.","oa_version":"Preprint","date_created":"2023-04-30T22:01:05Z","title":"Marked Length Spectral determination of analytic chaotic billiards with axial symmetries","arxiv":1,"publication_identifier":{"issn":["0020-9910"],"eissn":["1432-1297"]},"publication_status":"published"},{"doi":"10.1007/s40598-022-00200-7","oa":1,"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.","month":"06","department":[{"_id":"VaKa"}],"article_type":"original","project":[{"_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","call_identifier":"H2020","grant_number":"885707","name":"Spectral rigidity and integrability for billiards and geodesic flows"}],"volume":8,"author":[{"first_name":"Trevor","full_name":"Clark, Trevor","last_name":"Clark"},{"full_name":"Drach, Kostiantyn","last_name":"Drach","first_name":"Kostiantyn","id":"fe8209e2-906f-11eb-847d-950f8fc09115","orcid":"0000-0002-9156-8616"},{"last_name":"Kozlovski","full_name":"Kozlovski, Oleg","first_name":"Oleg"},{"first_name":"Sebastian Van","last_name":"Strien","full_name":"Strien, Sebastian Van"}],"publisher":"Springer Nature","article_processing_charge":"No","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"related_material":{"link":[{"url":"https://doi.org/10.1007/s40598-022-00209-y","relation":"erratum"},{"url":"https://doi.org/10.1007/s40598-022-00218-x","relation":"erratum"}]},"publication_status":"published","file":[{"creator":"kschuh","file_id":"11559","date_updated":"2022-07-12T10:04:55Z","relation":"main_file","checksum":"16e7c659dee9073c6c8aeb87316ef201","file_name":"2022_ArnoldMathematicalJournal_Clark.pdf","success":1,"content_type":"application/pdf","date_created":"2022-07-12T10:04:55Z","file_size":2509915,"access_level":"open_access"}],"publication_identifier":{"eissn":["2199-6806"],"issn":["2199-6792"]},"OA_type":"hybrid","oa_version":"Published Version","date_created":"2022-07-10T22:01:53Z","title":"The dynamics of complex box mappings","file_date_updated":"2022-07-12T10:04:55Z","date_updated":"2025-07-10T11:50:12Z","publication":"Arnold Mathematical Journal","page":"319-410","status":"public","scopus_import":"1","ec_funded":1,"issue":"2","quality_controlled":"1","type":"journal_article","_id":"11553","abstract":[{"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.","lang":"eng"}],"language":[{"iso":"eng"}],"citation":{"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>.","ista":"Clark T, Drach K, Kozlovski O, Strien SV. 2022. The dynamics of complex box mappings. Arnold Mathematical Journal. 8(2), 319–410.","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>","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>","short":"T. Clark, K. Drach, O. Kozlovski, S.V. Strien, Arnold Mathematical Journal 8 (2022) 319–410.","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.","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>."},"day":"01","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["500"],"year":"2022","intvolume":"         8","OA_place":"publisher","date_published":"2022-06-01T00:00:00Z"},{"oa":1,"doi":"10.1016/j.aim.2022.108591","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).","department":[{"_id":"VaKa"}],"month":"10","project":[{"grant_number":"885707","call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","name":"Spectral rigidity and integrability for billiards and geodesic flows"}],"article_type":"original","author":[{"last_name":"Drach","full_name":"Drach, Kostiantyn","orcid":"0000-0002-9156-8616","first_name":"Kostiantyn","id":"fe8209e2-906f-11eb-847d-950f8fc09115"},{"first_name":"Dierk","full_name":"Schleicher, Dierk","last_name":"Schleicher"}],"volume":408,"publisher":"Elsevier","article_processing_charge":"Yes (via OA deal)","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"corr_author":"1","publication_status":"published","file":[{"access_level":"open_access","date_created":"2023-02-02T07:39:09Z","file_size":2164036,"success":1,"content_type":"application/pdf","file_name":"2022_AdvancesMathematics_Drach.pdf","checksum":"2710e6f5820f8c20a676ddcbb30f0e8d","relation":"main_file","date_updated":"2023-02-02T07:39:09Z","creator":"dernst","file_id":"12474"}],"keyword":["General Mathematics"],"publication_identifier":{"issn":["0001-8708"]},"oa_version":"Published Version","date_created":"2022-08-01T17:08:16Z","title":"Rigidity of Newton dynamics","file_date_updated":"2023-02-02T07:39:09Z","isi":1,"publication":"Advances in Mathematics","date_updated":"2025-04-14T07:53:45Z","status":"public","scopus_import":"1","ec_funded":1,"issue":"Part A","quality_controlled":"1","type":"journal_article","external_id":{"isi":["000860924200005"]},"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."}],"_id":"11717","language":[{"iso":"eng"}],"citation":{"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>","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>","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>.","ieee":"K. Drach and D. Schleicher, “Rigidity of Newton dynamics,” <i>Advances in Mathematics</i>, vol. 408, no. Part A. Elsevier, 2022.","short":"K. Drach, D. Schleicher, Advances in Mathematics 408 (2022)."},"day":"29","has_accepted_license":"1","ddc":["510"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2022","intvolume":"       408","article_number":"108591","date_published":"2022-10-29T00:00:00Z"},{"page":"525-537","status":"public","scopus_import":"1","issue":"6","ec_funded":1,"isi":1,"publication":"Regular and Chaotic Dynamics","date_updated":"2025-04-14T07:53:45Z","year":"2022","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"        27","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.14640"}],"date_published":"2022-10-03T00:00:00Z","type":"journal_article","quality_controlled":"1","_id":"12145","language":[{"iso":"eng"}],"abstract":[{"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.","lang":"eng"}],"external_id":{"arxiv":["2105.14640"],"isi":["000865267300002"]},"day":"03","citation":{"short":"E. Koudjinan, V. Kaloshin, Regular and Chaotic Dynamics 27 (2022) 525–537.","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.","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>.","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.","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>."},"publisher":"Springer Nature","corr_author":"1","article_processing_charge":"No","related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1134/s1560354722060107"}]},"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).","oa":1,"doi":"10.1134/S1560354722050021","article_type":"original","project":[{"call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707","name":"Spectral rigidity and integrability for billiards and geodesic flows"}],"month":"10","department":[{"_id":"VaKa"}],"author":[{"full_name":"Koudjinan, Edmond","last_name":"Koudjinan","orcid":"0000-0003-2640-4049","first_name":"Edmond","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E"},{"orcid":"0000-0002-6051-2628","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","last_name":"Kaloshin"}],"volume":27,"arxiv":1,"publication_identifier":{"issn":["1560-3547"],"eissn":["1468-4845"]},"keyword":["Mechanical Engineering","Applied Mathematics","Mathematical Physics","Modeling and Simulation","Statistical and Nonlinear Physics","Mathematics (miscellaneous)"],"oa_version":"Preprint","title":"On some invariants of Birkhoff billiards under conjugacy","date_created":"2023-01-12T12:06:49Z","publication_status":"published"}]