---
_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
arxiv: 1
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.
    <i>Regular and Chaotic Dynamics</i>. 2022;27(6):525-537. 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>
  chicago: Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff
    Billiards under Conjugacy.” <i>Regular and Chaotic Dynamics</i>. Springer Nature,
    2022. <a href="https://doi.org/10.1134/S1560354722050021">https://doi.org/10.1134/S1560354722050021</a>.
  ieee: E. Koudjinan and V. Kaloshin, “On some invariants of Birkhoff billiards under
    conjugacy,” <i>Regular and Chaotic Dynamics</i>, vol. 27, no. 6. Springer Nature,
    pp. 525–537, 2022.
  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.” <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>.
  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'
...