---
_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
arxiv: 1
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. <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>
  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>
  chicago: De Simoi, Jacopo, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectral
    Determination of Analytic Chaotic Billiards with Axial Symmetries.” <i>Inventiones
    Mathematicae</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s00222-023-01191-8">https://doi.org/10.1007/s00222-023-01191-8</a>.
  ieee: J. De Simoi, V. Kaloshin, and M. Leguil, “Marked Length Spectral determination
    of analytic chaotic billiards with axial symmetries,” <i>Inventiones Mathematicae</i>,
    vol. 233. Springer Nature, pp. 829–901, 2023.
  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.” <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>.
  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: 2025-04-14T07:53:46Z
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'
...