---
_id: '8415'
abstract:
- lang: eng
  text: 'We consider billiards obtained by removing three strictly convex obstacles
    satisfying the non-eclipse condition on the plane. The restriction of the dynamics
    to the set of non-escaping orbits is conjugated to a subshift on three symbols
    that provides a natural labeling of all periodic orbits. We study the following
    inverse problem: does the Marked Length Spectrum (i.e., the set of lengths of
    periodic orbits together with their labeling), determine the geometry of the billiard
    table? We show that from the Marked Length Spectrum it is possible to recover
    the curvature at periodic points of period two, as well as the Lyapunov exponent
    of each periodic orbit.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Péter
  full_name: Bálint, Péter
  last_name: Bálint
- 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: Bálint P, De Simoi J, Kaloshin V, Leguil M. Marked length spectrum, homoclinic
    orbits and the geometry of open dispersing billiards. <i>Communications in Mathematical
    Physics</i>. 2019;374(3):1531-1575. doi:<a href="https://doi.org/10.1007/s00220-019-03448-x">10.1007/s00220-019-03448-x</a>
  apa: Bálint, P., De Simoi, J., Kaloshin, V., &#38; Leguil, M. (2019). Marked length
    spectrum, homoclinic orbits and the geometry of open dispersing billiards. <i>Communications
    in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s00220-019-03448-x">https://doi.org/10.1007/s00220-019-03448-x</a>
  chicago: Bálint, Péter, Jacopo De Simoi, Vadim Kaloshin, and Martin Leguil. “Marked
    Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.”
    <i>Communications in Mathematical Physics</i>. Springer Nature, 2019. <a href="https://doi.org/10.1007/s00220-019-03448-x">https://doi.org/10.1007/s00220-019-03448-x</a>.
  ieee: P. Bálint, J. De Simoi, V. Kaloshin, and M. Leguil, “Marked length spectrum,
    homoclinic orbits and the geometry of open dispersing billiards,” <i>Communications
    in Mathematical Physics</i>, vol. 374, no. 3. Springer Nature, pp. 1531–1575,
    2019.
  ista: Bálint P, De Simoi J, Kaloshin V, Leguil M. 2019. Marked length spectrum,
    homoclinic orbits and the geometry of open dispersing billiards. Communications
    in Mathematical Physics. 374(3), 1531–1575.
  mla: Bálint, Péter, et al. “Marked Length Spectrum, Homoclinic Orbits and the Geometry
    of Open Dispersing Billiards.” <i>Communications in Mathematical Physics</i>,
    vol. 374, no. 3, Springer Nature, 2019, pp. 1531–75, doi:<a href="https://doi.org/10.1007/s00220-019-03448-x">10.1007/s00220-019-03448-x</a>.
  short: P. Bálint, J. De Simoi, V. Kaloshin, M. Leguil, Communications in Mathematical
    Physics 374 (2019) 1531–1575.
date_created: 2020-09-17T10:41:27Z
date_published: 2019-05-09T00:00:00Z
date_updated: 2021-01-12T08:19:08Z
day: '09'
doi: 10.1007/s00220-019-03448-x
extern: '1'
external_id:
  arxiv:
  - '1809.08947'
intvolume: '       374'
issue: '3'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1809.08947
month: '05'
oa: 1
oa_version: Preprint
page: 1531-1575
publication: Communications in Mathematical Physics
publication_identifier:
  issn:
  - 0010-3616
  - 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Marked length spectrum, homoclinic orbits and the geometry of open dispersing
  billiards
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 374
year: '2019'
...