[{"ec_funded":1,"year":"2023","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.","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"VaKa"}],"author":[{"last_name":"De Simoi","first_name":"Jacopo","full_name":"De Simoi, Jacopo"},{"orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim","full_name":"Kaloshin, Vadim"},{"full_name":"Leguil, Martin","first_name":"Martin","last_name":"Leguil"}],"date_created":"2023-04-30T22:01:05Z","date_updated":"2023-10-04T11:25:37Z","volume":233,"month":"08","publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1905.00890"}],"external_id":{"isi":["000978887600001"],"arxiv":["1905.00890"]},"oa":1,"isi":1,"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Spectral rigidity and integrability for billiards and geodesic flows","grant_number":"885707","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A"}],"doi":"10.1007/s00222-023-01191-8","language":[{"iso":"eng"}],"type":"journal_article","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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12877","status":"public","title":"Marked Length Spectral determination of analytic chaotic billiards with axial symmetries","intvolume":" 233","oa_version":"Preprint","scopus_import":"1","day":"01","article_processing_charge":"No","publication":"Inventiones Mathematicae","citation":{"short":"J. De Simoi, V. Kaloshin, M. Leguil, Inventiones Mathematicae 233 (2023) 829–901.","mla":"De Simoi, Jacopo, et al. “Marked Length Spectral Determination of Analytic Chaotic Billiards with Axial Symmetries.” Inventiones Mathematicae, vol. 233, Springer Nature, 2023, pp. 829–901, doi:10.1007/s00222-023-01191-8.","chicago":"De Simoi, Jacopo, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectral Determination of Analytic Chaotic Billiards with Axial Symmetries.” Inventiones Mathematicae. Springer Nature, 2023. https://doi.org/10.1007/s00222-023-01191-8.","ama":"De Simoi J, Kaloshin V, Leguil M. Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. Inventiones Mathematicae. 2023;233:829-901. doi:10.1007/s00222-023-01191-8","ieee":"J. De Simoi, V. Kaloshin, and M. Leguil, “Marked Length Spectral determination of analytic chaotic billiards with axial symmetries,” Inventiones Mathematicae, vol. 233. Springer Nature, pp. 829–901, 2023.","apa":"De Simoi, J., Kaloshin, V., & Leguil, M. (2023). Marked Length Spectral determination of analytic chaotic billiards with axial symmetries. Inventiones Mathematicae. Springer Nature. https://doi.org/10.1007/s00222-023-01191-8","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."},"article_type":"original","page":"829-901","date_published":"2023-08-01T00:00:00Z"},{"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."}],"type":"journal_article","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"14427","status":"public","title":"Length spectrum rigidity for piecewise analytic Bunimovich billiards","day":"29","article_processing_charge":"No","scopus_import":"1","date_published":"2023-09-29T00:00:00Z","publication":"Communications in Mathematical Physics","citation":{"ama":"Chen J, Kaloshin V, Zhang HK. Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics. 2023. doi:10.1007/s00220-023-04837-z","ista":"Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics.","ieee":"J. Chen, V. Kaloshin, and H. K. Zhang, “Length spectrum rigidity for piecewise analytic Bunimovich billiards,” Communications in Mathematical Physics. Springer Nature, 2023.","apa":"Chen, J., Kaloshin, V., & Zhang, H. K. (2023). Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04837-z","mla":"Chen, Jianyu, et al. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards.” Communications in Mathematical Physics, Springer Nature, 2023, doi:10.1007/s00220-023-04837-z.","short":"J. Chen, V. Kaloshin, H.K. Zhang, Communications in Mathematical Physics (2023).","chicago":"Chen, Jianyu, Vadim Kaloshin, and Hong Kun Zhang. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards.” Communications in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04837-z."},"article_type":"original","ec_funded":1,"author":[{"full_name":"Chen, Jianyu","last_name":"Chen","first_name":"Jianyu"},{"full_name":"Kaloshin, Vadim","first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628"},{"last_name":"Zhang","first_name":"Hong Kun","full_name":"Zhang, Hong Kun"}],"date_updated":"2023-12-13T13:02:44Z","date_created":"2023-10-15T22:01:11Z","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).","year":"2023","publication_status":"epub_ahead","department":[{"_id":"VaKa"}],"publisher":"Springer Nature","month":"09","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"doi":"10.1007/s00220-023-04837-z","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.07330"}],"external_id":{"arxiv":["1902.07330"],"isi":["001073177200001"]},"isi":1,"quality_controlled":"1","project":[{"_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707","name":"Spectral rigidity and integrability for billiards and geodesic flows","call_identifier":"H2020"}]},{"scopus_import":"1","day":"01","article_processing_charge":"No","has_accepted_license":"1","publication":"Arnold Mathematical Journal","citation":{"ieee":"T. Clark, K. Drach, O. Kozlovski, and S. V. Strien, “The dynamics of complex box mappings,” Arnold Mathematical Journal, vol. 8, no. 2. Springer Nature, pp. 319–410, 2022.","apa":"Clark, T., Drach, K., Kozlovski, O., & Strien, S. V. (2022). The dynamics of complex box mappings. Arnold Mathematical Journal. Springer Nature. https://doi.org/10.1007/s40598-022-00200-7","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. Arnold Mathematical Journal. 2022;8(2):319-410. doi:10.1007/s40598-022-00200-7","chicago":"Clark, Trevor, Kostiantyn Drach, Oleg Kozlovski, and Sebastian Van Strien. “The Dynamics of Complex Box Mappings.” Arnold Mathematical Journal. Springer Nature, 2022. https://doi.org/10.1007/s40598-022-00200-7.","short":"T. Clark, K. Drach, O. Kozlovski, S.V. Strien, Arnold Mathematical Journal 8 (2022) 319–410.","mla":"Clark, Trevor, et al. “The Dynamics of Complex Box Mappings.” Arnold Mathematical Journal, vol. 8, no. 2, Springer Nature, 2022, pp. 319–410, doi:10.1007/s40598-022-00200-7."},"article_type":"original","page":"319-410","date_published":"2022-06-01T00:00:00Z","type":"journal_article","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"}],"issue":"2","_id":"11553","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"The dynamics of complex box mappings","ddc":["500"],"status":"public","intvolume":" 8","oa_version":"None","file":[{"file_id":"11559","relation":"main_file","success":1,"checksum":"16e7c659dee9073c6c8aeb87316ef201","date_created":"2022-07-12T10:04:55Z","date_updated":"2022-07-12T10:04:55Z","access_level":"open_access","file_name":"2022_ArnoldMathematicalJournal_Clark.pdf","creator":"kschuh","content_type":"application/pdf","file_size":2509915}],"month":"06","publication_identifier":{"eissn":["2199-6806"],"issn":["2199-6792"]},"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","project":[{"grant_number":"885707","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","name":"Spectral rigidity and integrability for billiards and geodesic flows","call_identifier":"H2020"}],"doi":"10.1007/s40598-022-00200-7","language":[{"iso":"eng"}],"file_date_updated":"2022-07-12T10:04:55Z","ec_funded":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.","year":"2022","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"VaKa"}],"author":[{"first_name":"Trevor","last_name":"Clark","full_name":"Clark, Trevor"},{"full_name":"Drach, Kostiantyn","orcid":"0000-0002-9156-8616","id":"fe8209e2-906f-11eb-847d-950f8fc09115","last_name":"Drach","first_name":"Kostiantyn"},{"last_name":"Kozlovski","first_name":"Oleg","full_name":"Kozlovski, Oleg"},{"full_name":"Strien, Sebastian Van","last_name":"Strien","first_name":"Sebastian Van"}],"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"}]},"date_created":"2022-07-10T22:01:53Z","date_updated":"2023-02-16T10:02:12Z","volume":8},{"scopus_import":"1","article_processing_charge":"No","day":"01","citation":{"apa":"Bialy, M., Fiorebe, C., Glutsyuk, A., Levi, M., Plakhov, A., & Tabachnikov, S. (2022). Open problems on billiards and geometric optics. Arnold Mathematical Journal. Hybrid: Springer Nature. https://doi.org/10.1007/s40598-022-00198-y","ieee":"M. Bialy, C. Fiorebe, A. Glutsyuk, M. Levi, A. Plakhov, and S. Tabachnikov, “Open problems on billiards and geometric optics,” Arnold Mathematical Journal, vol. 8. Springer Nature, pp. 411–422, 2022.","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.","ama":"Bialy M, Fiorebe C, Glutsyuk A, Levi M, Plakhov A, Tabachnikov S. Open problems on billiards and geometric optics. Arnold Mathematical Journal. 2022;8:411-422. doi:10.1007/s40598-022-00198-y","chicago":"Bialy, Misha, Corentin Fiorebe, Alexey Glutsyuk, Mark Levi, Alexander Plakhov, and Serge Tabachnikov. “Open Problems on Billiards and Geometric Optics.” Arnold Mathematical Journal. Springer Nature, 2022. https://doi.org/10.1007/s40598-022-00198-y.","short":"M. Bialy, C. Fiorebe, A. Glutsyuk, M. Levi, A. Plakhov, S. Tabachnikov, Arnold Mathematical Journal 8 (2022) 411–422.","mla":"Bialy, Misha, et al. “Open Problems on Billiards and Geometric Optics.” Arnold Mathematical Journal, vol. 8, Springer Nature, 2022, pp. 411–22, doi:10.1007/s40598-022-00198-y."},"publication":"Arnold Mathematical Journal","page":"411-422","article_type":"original","date_published":"2022-10-01T00:00:00Z","type":"journal_article","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."}],"_id":"10706","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 8","status":"public","title":"Open problems on billiards and geometric optics","oa_version":"Preprint","publication_identifier":{"eissn":["2199-6806"],"issn":["2199-6792"]},"month":"10","external_id":{"arxiv":["2110.10750"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2110.10750"}],"quality_controlled":"1","doi":"10.1007/s40598-022-00198-y","conference":{"name":"CIRM: Centre International de Rencontres Mathématiques","start_date":"2021-10-04","location":"Hybrid","end_date":"2021-10-08"},"language":[{"iso":"eng"}],"year":"2022","publisher":"Springer Nature","department":[{"_id":"VaKa"}],"publication_status":"published","related_material":{"link":[{"url":"https://conferences.cirm-math.fr/2383.html","relation":"earlier_version"}]},"author":[{"full_name":"Bialy, Misha","first_name":"Misha","last_name":"Bialy"},{"first_name":"Corentin","last_name":"Fiorebe","id":"06619f18-9070-11eb-847d-d1ee780bd88b","full_name":"Fiorebe, Corentin"},{"last_name":"Glutsyuk","first_name":"Alexey","full_name":"Glutsyuk, Alexey"},{"last_name":"Levi","first_name":"Mark","full_name":"Levi, Mark"},{"last_name":"Plakhov","first_name":"Alexander","full_name":"Plakhov, Alexander"},{"full_name":"Tabachnikov, Serge","first_name":"Serge","last_name":"Tabachnikov"}],"volume":8,"date_created":"2022-01-30T23:01:34Z","date_updated":"2023-02-27T07:34:08Z"},{"type":"journal_article","issue":"Part A","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","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 408","title":"Rigidity of Newton dynamics","status":"public","ddc":["510"],"file":[{"content_type":"application/pdf","file_size":2164036,"creator":"dernst","file_name":"2022_AdvancesMathematics_Drach.pdf","access_level":"open_access","date_updated":"2023-02-02T07:39:09Z","date_created":"2023-02-02T07:39:09Z","checksum":"2710e6f5820f8c20a676ddcbb30f0e8d","success":1,"relation":"main_file","file_id":"12474"}],"oa_version":"Published Version","scopus_import":"1","keyword":["General Mathematics"],"has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"29","citation":{"chicago":"Drach, Kostiantyn, and Dierk Schleicher. “Rigidity of Newton Dynamics.” Advances in Mathematics. Elsevier, 2022. https://doi.org/10.1016/j.aim.2022.108591.","mla":"Drach, Kostiantyn, and Dierk Schleicher. “Rigidity of Newton Dynamics.” Advances in Mathematics, vol. 408, no. Part A, 108591, Elsevier, 2022, doi:10.1016/j.aim.2022.108591.","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.","ieee":"K. Drach and D. Schleicher, “Rigidity of Newton dynamics,” Advances in Mathematics, vol. 408, no. Part A. Elsevier, 2022.","apa":"Drach, K., & Schleicher, D. (2022). Rigidity of Newton dynamics. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2022.108591","ama":"Drach K, Schleicher D. Rigidity of Newton dynamics. Advances in Mathematics. 2022;408(Part A). doi:10.1016/j.aim.2022.108591"},"publication":"Advances in Mathematics","article_type":"original","date_published":"2022-10-29T00:00:00Z","article_number":"108591","ec_funded":1,"file_date_updated":"2023-02-02T07:39:09Z","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).","year":"2022","department":[{"_id":"VaKa"}],"publisher":"Elsevier","publication_status":"published","author":[{"full_name":"Drach, Kostiantyn","last_name":"Drach","first_name":"Kostiantyn","orcid":"0000-0002-9156-8616","id":"fe8209e2-906f-11eb-847d-950f8fc09115"},{"full_name":"Schleicher, Dierk","last_name":"Schleicher","first_name":"Dierk"}],"volume":408,"date_created":"2022-08-01T17:08:16Z","date_updated":"2023-08-03T12:36:07Z","publication_identifier":{"issn":["0001-8708"]},"month":"10","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000860924200005"]},"project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707"}],"quality_controlled":"1","isi":1,"doi":"10.1016/j.aim.2022.108591","language":[{"iso":"eng"}]},{"scopus_import":"1","keyword":["Mechanical Engineering","Applied Mathematics","Mathematical Physics","Modeling and Simulation","Statistical and Nonlinear Physics","Mathematics (miscellaneous)"],"day":"03","article_processing_charge":"No","publication":"Regular and Chaotic Dynamics","citation":{"ista":"Koudjinan E, Kaloshin V. 2022. On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. 27(6), 525–537.","apa":"Koudjinan, E., & Kaloshin, V. (2022). On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. Springer Nature. https://doi.org/10.1134/S1560354722050021","ieee":"E. Koudjinan and V. Kaloshin, “On some invariants of Birkhoff billiards under conjugacy,” Regular and Chaotic Dynamics, vol. 27, no. 6. Springer Nature, pp. 525–537, 2022.","ama":"Koudjinan E, Kaloshin V. On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. 2022;27(6):525-537. doi:10.1134/S1560354722050021","chicago":"Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards under Conjugacy.” Regular and Chaotic Dynamics. Springer Nature, 2022. https://doi.org/10.1134/S1560354722050021.","mla":"Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards under Conjugacy.” Regular and Chaotic Dynamics, vol. 27, no. 6, Springer Nature, 2022, pp. 525–37, doi:10.1134/S1560354722050021.","short":"E. Koudjinan, V. Kaloshin, Regular and Chaotic Dynamics 27 (2022) 525–537."},"article_type":"original","page":"525-537","date_published":"2022-10-03T00:00:00Z","type":"journal_article","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."}],"issue":"6","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"12145","status":"public","title":"On some invariants of Birkhoff billiards under conjugacy","intvolume":" 27","oa_version":"Preprint","month":"10","publication_identifier":{"issn":["1560-3547"],"eissn":["1468-4845"]},"oa":1,"external_id":{"arxiv":["2105.14640"],"isi":["000865267300002"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.14640","open_access":"1"}],"isi":1,"quality_controlled":"1","project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707"}],"doi":"10.1134/S1560354722050021","language":[{"iso":"eng"}],"ec_funded":1,"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).","year":"2022","publication_status":"published","department":[{"_id":"VaKa"}],"publisher":"Springer Nature","author":[{"full_name":"Koudjinan, Edmond","last_name":"Koudjinan","first_name":"Edmond","orcid":"0000-0003-2640-4049","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E"},{"full_name":"Kaloshin, Vadim","first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628"}],"related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1134/s1560354722060107"}]},"date_created":"2023-01-12T12:06:49Z","date_updated":"2023-08-04T08:59:14Z","volume":27},{"has_accepted_license":"1","article_processing_charge":"No","citation":{"short":"V. Kaloshin, E. Koudjinan, (2021).","mla":"Kaloshin, Vadim, and Edmond Koudjinan. Non Co-Preservation of the 1/2 and 1/(2l+1)-Rational Caustics along Deformations of Circles. 2021.","chicago":"Kaloshin, Vadim, and Edmond Koudjinan. “Non Co-Preservation of the 1/2 and 1/(2l+1)-Rational Caustics along Deformations of Circles,” 2021.","ama":"Kaloshin V, Koudjinan E. Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations of circles. 2021.","apa":"Kaloshin, V., & Koudjinan, E. (2021). Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations of circles.","ieee":"V. Kaloshin and E. Koudjinan, “Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations of circles.” 2021.","ista":"Kaloshin V, Koudjinan E. 2021. Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations of circles."},"oa":1,"date_published":"2021-01-01T00:00:00Z","language":[{"iso":"eng"}],"type":"preprint","file_date_updated":"2021-05-30T13:57:37Z","abstract":[{"text":"For any given positive integer l, we prove that every plane deformation of a circlewhich preserves the 1/2and 1/ (2l + 1) -rational caustics is trivial i.e. the deformationconsists only of similarities (rescalings and isometries).","lang":"eng"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"9435","year":"2021","department":[{"_id":"VaKa"}],"title":"Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations of circles","ddc":["500"],"status":"public","author":[{"full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim"},{"first_name":"Edmond","last_name":"Koudjinan","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","orcid":"0000-0003-2640-4049","full_name":"Koudjinan, Edmond"}],"oa_version":"Submitted Version","file":[{"checksum":"b281b5c2e3e90de0646c3eafcb2c6c25","date_updated":"2021-05-30T13:57:37Z","date_created":"2021-05-30T13:57:37Z","relation":"main_file","file_id":"9436","file_size":353431,"content_type":"application/pdf","creator":"ekoudjin","access_level":"open_access","file_name":"CoExistence 2&3 caustics 3_17_6_2_3.pdf"}],"date_updated":"2021-06-01T09:10:22Z","date_created":"2021-05-30T13:58:13Z"},{"language":[{"iso":"eng"}],"doi":"10.1134/S1560354721010044","isi":1,"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/2010.13243","open_access":"1"}],"external_id":{"isi":["000614454700004"],"arxiv":["2010.13243"]},"oa":1,"publication_identifier":{"issn":["1560-3547"]},"month":"02","volume":26,"date_created":"2020-10-21T14:56:47Z","date_updated":"2023-08-07T13:37:27Z","author":[{"full_name":"Chierchia, Luigi","last_name":"Chierchia","first_name":"Luigi"},{"full_name":"Koudjinan, Edmond","last_name":"Koudjinan","first_name":"Edmond","orcid":"0000-0003-2640-4049","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E"}],"publisher":"Springer Nature","department":[{"_id":"VaKa"}],"publication_status":"published","year":"2021","date_published":"2021-02-03T00:00:00Z","page":"61-88","article_type":"original","citation":{"ama":"Chierchia L, Koudjinan E. V.I. Arnold’s “‘Global’” KAM theorem and geometric measure estimates. Regular and Chaotic Dynamics. 2021;26(1):61-88. doi:10.1134/S1560354721010044","ista":"Chierchia L, Koudjinan E. 2021. V.I. Arnold’s ‘“Global”’ KAM theorem and geometric measure estimates. Regular and Chaotic Dynamics. 26(1), 61–88.","ieee":"L. Chierchia and E. Koudjinan, “V.I. Arnold’s ‘“Global”’ KAM theorem and geometric measure estimates,” Regular and Chaotic Dynamics, vol. 26, no. 1. Springer Nature, pp. 61–88, 2021.","apa":"Chierchia, L., & Koudjinan, E. (2021). V.I. Arnold’s “‘Global’” KAM theorem and geometric measure estimates. Regular and Chaotic Dynamics. Springer Nature. https://doi.org/10.1134/S1560354721010044","mla":"Chierchia, Luigi, and Edmond Koudjinan. “V.I. Arnold’s ‘“Global”’ KAM Theorem and Geometric Measure Estimates.” Regular and Chaotic Dynamics, vol. 26, no. 1, Springer Nature, 2021, pp. 61–88, doi:10.1134/S1560354721010044.","short":"L. Chierchia, E. Koudjinan, Regular and Chaotic Dynamics 26 (2021) 61–88.","chicago":"Chierchia, Luigi, and Edmond Koudjinan. “V.I. Arnold’s ‘“Global”’ KAM Theorem and Geometric Measure Estimates.” Regular and Chaotic Dynamics. Springer Nature, 2021. https://doi.org/10.1134/S1560354721010044."},"publication":"Regular and Chaotic Dynamics","article_processing_charge":"No","day":"03","keyword":["Nearly{integrable Hamiltonian systems","perturbation theory","KAM Theory","Arnold's scheme","Kolmogorov's set","primary invariant tori","Lagrangian tori","measure estimates","small divisors","integrability on nowhere dense sets","Diophantine frequencies."],"scopus_import":"1","oa_version":"Preprint","intvolume":" 26","status":"public","title":"V.I. Arnold's ''Global'' KAM theorem and geometric measure estimates","ddc":["515"],"_id":"8689","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"1","abstract":[{"text":"This paper continues the discussion started in [CK19] concerning Arnold's legacy on classical KAM theory and (some of) its modern developments. We prove a detailed and explicit `global' Arnold's KAM Theorem, which yields, in particular, the Whitney conjugacy of a non{degenerate, real{analytic, nearly-integrable Hamiltonian system to an integrable system on a closed, nowhere dense, positive measure subset of the phase space. Detailed measure estimates on the Kolmogorov's set are provided in the case the phase space is: (A) a uniform neighbourhood of an arbitrary (bounded) set times the d-torus and (B) a domain with C2 boundary times the d-torus. All constants are explicitly given.","lang":"eng"}],"type":"journal_article"}]