--- _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. 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.' article_processing_charge: No article_type: original author: - first_name: Jacopo full_name: De Simoi, Jacopo last_name: De Simoi - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: Martin full_name: Leguil, Martin last_name: Leguil citation: 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 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 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. 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. 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. 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. short: J. De Simoi, V. Kaloshin, M. Leguil, Inventiones Mathematicae 233 (2023) 829–901. date_created: 2023-04-30T22:01:05Z date_published: 2023-08-01T00:00:00Z date_updated: 2023-10-04T11:25:37Z day: '01' department: - _id: VaKa doi: 10.1007/s00222-023-01191-8 ec_funded: 1 external_id: arxiv: - '1905.00890' isi: - '000978887600001' intvolume: ' 233' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.1905.00890 month: '08' oa: 1 oa_version: Preprint page: 829-901 project: - _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A call_identifier: H2020 grant_number: '885707' name: Spectral rigidity and integrability for billiards and geodesic flows publication: Inventiones Mathematicae publication_identifier: eissn: - 1432-1297 issn: - 0020-9910 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Marked Length Spectral determination of analytic chaotic billiards with axial symmetries type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 233 year: '2023' ... --- _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. 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).' article_processing_charge: No article_type: original author: - first_name: Jianyu full_name: Chen, Jianyu last_name: Chen - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: Hong Kun full_name: Zhang, Hong Kun last_name: Zhang 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 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 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. ieee: J. Chen, V. Kaloshin, and H. K. Zhang, “Length spectrum rigidity for piecewise analytic Bunimovich billiards,” Communications in Mathematical Physics. Springer Nature, 2023. ista: Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics. 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). date_created: 2023-10-15T22:01:11Z date_published: 2023-09-29T00:00:00Z date_updated: 2023-12-13T13:02:44Z day: '29' department: - _id: VaKa doi: 10.1007/s00220-023-04837-z ec_funded: 1 external_id: arxiv: - '1902.07330' isi: - '001073177200001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1902.07330 month: '09' oa: 1 oa_version: Preprint project: - _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A call_identifier: H2020 grant_number: '885707' name: Spectral rigidity and integrability for billiards and geodesic flows publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Length spectrum rigidity for piecewise analytic Bunimovich billiards type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '11553' 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." 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. article_processing_charge: No article_type: original author: - first_name: Trevor full_name: Clark, Trevor last_name: Clark - first_name: Kostiantyn full_name: Drach, Kostiantyn id: fe8209e2-906f-11eb-847d-950f8fc09115 last_name: Drach orcid: 0000-0002-9156-8616 - first_name: Oleg full_name: Kozlovski, Oleg last_name: Kozlovski - first_name: Sebastian Van full_name: Strien, Sebastian Van last_name: Strien citation: 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 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 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. 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. ista: Clark T, Drach K, Kozlovski O, Strien SV. 2022. The dynamics of complex box mappings. Arnold Mathematical Journal. 8(2), 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. short: T. Clark, K. Drach, O. Kozlovski, S.V. Strien, Arnold Mathematical Journal 8 (2022) 319–410. date_created: 2022-07-10T22:01:53Z date_published: 2022-06-01T00:00:00Z date_updated: 2023-02-16T10:02:12Z day: '01' ddc: - '500' department: - _id: VaKa doi: 10.1007/s40598-022-00200-7 ec_funded: 1 file: - access_level: open_access checksum: 16e7c659dee9073c6c8aeb87316ef201 content_type: application/pdf creator: kschuh date_created: 2022-07-12T10:04:55Z date_updated: 2022-07-12T10:04:55Z file_id: '11559' file_name: 2022_ArnoldMathematicalJournal_Clark.pdf file_size: 2509915 relation: main_file success: 1 file_date_updated: 2022-07-12T10:04:55Z has_accepted_license: '1' intvolume: ' 8' issue: '2' language: - iso: eng month: '06' oa: 1 oa_version: None page: 319-410 project: - _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A call_identifier: H2020 grant_number: '885707' name: Spectral rigidity and integrability for billiards and geodesic flows publication: Arnold Mathematical Journal publication_identifier: eissn: - 2199-6806 issn: - 2199-6792 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: link: - relation: erratum url: https://doi.org/10.1007/s40598-022-00209-y - relation: erratum url: https://doi.org/10.1007/s40598-022-00218-x scopus_import: '1' status: public title: The dynamics of complex box mappings tmp: 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) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 8 year: '2022' ... --- _id: '10706' 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_processing_charge: No article_type: original author: - first_name: Misha full_name: Bialy, Misha last_name: Bialy - first_name: Corentin full_name: Fiorebe, Corentin id: 06619f18-9070-11eb-847d-d1ee780bd88b last_name: Fiorebe - first_name: Alexey full_name: Glutsyuk, Alexey last_name: Glutsyuk - first_name: Mark full_name: Levi, Mark last_name: Levi - first_name: Alexander full_name: Plakhov, Alexander last_name: Plakhov - first_name: Serge full_name: Tabachnikov, Serge last_name: Tabachnikov citation: 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 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' 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. 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. 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. short: M. Bialy, C. Fiorebe, A. Glutsyuk, M. Levi, A. Plakhov, S. Tabachnikov, Arnold Mathematical Journal 8 (2022) 411–422. conference: end_date: 2021-10-08 location: Hybrid name: 'CIRM: Centre International de Rencontres Mathématiques' start_date: 2021-10-04 date_created: 2022-01-30T23:01:34Z date_published: 2022-10-01T00:00:00Z date_updated: 2023-02-27T07:34:08Z day: '01' department: - _id: VaKa doi: 10.1007/s40598-022-00198-y external_id: arxiv: - '2110.10750' intvolume: ' 8' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2110.10750 month: '10' oa: 1 oa_version: Preprint page: 411-422 publication: Arnold Mathematical Journal publication_identifier: eissn: - 2199-6806 issn: - 2199-6792 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: link: - relation: earlier_version url: https://conferences.cirm-math.fr/2383.html scopus_import: '1' status: public title: Open problems on billiards and geometric optics type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 8 year: '2022' ... --- _id: '11717' 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." 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).' article_number: '108591' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Kostiantyn full_name: Drach, Kostiantyn id: fe8209e2-906f-11eb-847d-950f8fc09115 last_name: Drach orcid: 0000-0002-9156-8616 - first_name: Dierk full_name: Schleicher, Dierk last_name: Schleicher citation: ama: Drach K, Schleicher D. Rigidity of Newton dynamics. Advances in Mathematics. 2022;408(Part A). doi:10.1016/j.aim.2022.108591 apa: Drach, K., & Schleicher, D. (2022). Rigidity of Newton dynamics. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2022.108591 chicago: Drach, Kostiantyn, and Dierk Schleicher. “Rigidity of Newton Dynamics.” Advances in Mathematics. Elsevier, 2022. https://doi.org/10.1016/j.aim.2022.108591. ieee: K. Drach and D. Schleicher, “Rigidity of Newton dynamics,” Advances in Mathematics, vol. 408, no. Part A. Elsevier, 2022. ista: Drach K, Schleicher D. 2022. Rigidity of Newton dynamics. Advances in Mathematics. 408(Part A), 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). date_created: 2022-08-01T17:08:16Z date_published: 2022-10-29T00:00:00Z date_updated: 2023-08-03T12:36:07Z day: '29' ddc: - '510' department: - _id: VaKa doi: 10.1016/j.aim.2022.108591 ec_funded: 1 external_id: isi: - '000860924200005' file: - access_level: open_access checksum: 2710e6f5820f8c20a676ddcbb30f0e8d content_type: application/pdf creator: dernst date_created: 2023-02-02T07:39:09Z date_updated: 2023-02-02T07:39:09Z file_id: '12474' file_name: 2022_AdvancesMathematics_Drach.pdf file_size: 2164036 relation: main_file success: 1 file_date_updated: 2023-02-02T07:39:09Z has_accepted_license: '1' intvolume: ' 408' isi: 1 issue: Part A keyword: - General Mathematics language: - iso: eng month: '10' oa: 1 oa_version: Published Version project: - _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A call_identifier: H2020 grant_number: '885707' name: Spectral rigidity and integrability for billiards and geodesic flows publication: Advances in Mathematics publication_identifier: issn: - 0001-8708 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Rigidity of Newton dynamics tmp: 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) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 408 year: '2022' ... --- _id: '12145' 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. 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)." article_processing_charge: No article_type: original author: - first_name: Edmond full_name: Koudjinan, Edmond id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E last_name: Koudjinan orcid: 0000-0003-2640-4049 - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 citation: 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 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 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. 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. ista: Koudjinan E, Kaloshin V. 2022. On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. 27(6), 525–537. 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. date_created: 2023-01-12T12:06:49Z date_published: 2022-10-03T00:00:00Z date_updated: 2023-08-04T08:59:14Z day: '03' department: - _id: VaKa doi: 10.1134/S1560354722050021 ec_funded: 1 external_id: arxiv: - '2105.14640' isi: - '000865267300002' intvolume: ' 27' isi: 1 issue: '6' keyword: - Mechanical Engineering - Applied Mathematics - Mathematical Physics - Modeling and Simulation - Statistical and Nonlinear Physics - Mathematics (miscellaneous) language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2105.14640 month: '10' oa: 1 oa_version: Preprint page: 525-537 project: - _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A call_identifier: H2020 grant_number: '885707' name: Spectral rigidity and integrability for billiards and geodesic flows publication: Regular and Chaotic Dynamics publication_identifier: eissn: - 1468-4845 issn: - 1560-3547 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: link: - relation: erratum url: https://doi.org/10.1134/s1560354722060107 scopus_import: '1' status: public title: On some invariants of Birkhoff billiards under conjugacy type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 27 year: '2022' ... --- _id: '9435' abstract: - lang: eng 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). article_processing_charge: No author: - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: Edmond full_name: Koudjinan, Edmond id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E last_name: Koudjinan orcid: 0000-0003-2640-4049 citation: 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. chicago: Kaloshin, Vadim, and Edmond Koudjinan. “Non Co-Preservation of the 1/2 and  1/(2l+1)-Rational Caustics along Deformations of Circles,” 2021. 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. mla: Kaloshin, Vadim, and Edmond Koudjinan. Non Co-Preservation of the 1/2 and  1/(2l+1)-Rational Caustics along Deformations of Circles. 2021. short: V. Kaloshin, E. Koudjinan, (2021). date_created: 2021-05-30T13:58:13Z date_published: 2021-01-01T00:00:00Z date_updated: 2021-06-01T09:10:22Z ddc: - '500' department: - _id: VaKa file: - access_level: open_access checksum: b281b5c2e3e90de0646c3eafcb2c6c25 content_type: application/pdf creator: ekoudjin date_created: 2021-05-30T13:57:37Z date_updated: 2021-05-30T13:57:37Z file_id: '9436' file_name: CoExistence 2&3 caustics 3_17_6_2_3.pdf file_size: 353431 relation: main_file file_date_updated: 2021-05-30T13:57:37Z has_accepted_license: '1' language: - iso: eng oa: 1 oa_version: Submitted Version status: public title: Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations of circles type: preprint user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '8689' abstract: - lang: eng 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.' article_processing_charge: No article_type: original author: - first_name: Luigi full_name: Chierchia, Luigi last_name: Chierchia - first_name: Edmond full_name: Koudjinan, Edmond id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E last_name: Koudjinan orcid: 0000-0003-2640-4049 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 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 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. 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. 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. 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. date_created: 2020-10-21T14:56:47Z date_published: 2021-02-03T00:00:00Z date_updated: 2023-08-07T13:37:27Z day: '03' ddc: - '515' department: - _id: VaKa doi: 10.1134/S1560354721010044 external_id: arxiv: - '2010.13243' isi: - '000614454700004' intvolume: ' 26' isi: 1 issue: '1' 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. language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2010.13243 month: '02' oa: 1 oa_version: Preprint page: 61-88 publication: Regular and Chaotic Dynamics publication_identifier: issn: - 1560-3547 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: V.I. Arnold's ''Global'' KAM theorem and geometric measure estimates type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 26 year: '2021' ...