---
_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
arxiv: 1
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. <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>
  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>
  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>.
  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.
  ista: Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise
    analytic Bunimovich billiards. Communications in Mathematical Physics. 404, 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>.
  short: J. Chen, V. Kaloshin, H.K. Zhang, Communications in Mathematical Physics
    404 (2023) 1–50.
corr_author: '1'
date_created: 2023-10-15T22:01:11Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2025-04-14T07:53:45Z
day: '01'
department:
- _id: VaKa
doi: 10.1007/s00220-023-04837-z
ec_funded: 1
external_id:
  arxiv:
  - '1902.07330'
  isi:
  - '001073177200001'
intvolume: '       404'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1902.07330
month: '11'
oa: 1
oa_version: Preprint
page: 1-50
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: published
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
volume: 404
year: '2023'
...