---
OA_type: free access
_id: '17231'
abstract:
- lang: eng
  text: In the class of projective billiards, which contains the usual billiards,
    we exhibit counter-examples to Ivrii's conjecture, which states that in any planar
    billiard with smooth boundary the set of periodic orbits has zero measure. The
    counter-examples are polygons admitting a 2-parameters family of n-periodic orbits,
    with n being either 3 or any even integer greater than 4.
article_processing_charge: No
article_type: original
author:
- first_name: Corentin
  full_name: Fiorebe, Corentin
  id: 06619f18-9070-11eb-847d-d1ee780bd88b
  last_name: Fiorebe
citation:
  ama: Fiorebe C. Examples of projective billiards with open sets of periodic orbits.
    <i>Discrete and Continuous Dynamical Systems- Series A</i>. 2024;44(11):3287-3301.
    doi:<a href="https://doi.org/10.3934/dcds.2024059">10.3934/dcds.2024059</a>
  apa: Fiorebe, C. (2024). Examples of projective billiards with open sets of periodic
    orbits. <i>Discrete and Continuous Dynamical Systems- Series A</i>. American Institute
    of Mathematical Sciences. <a href="https://doi.org/10.3934/dcds.2024059">https://doi.org/10.3934/dcds.2024059</a>
  chicago: Fiorebe, Corentin. “Examples of Projective Billiards with Open Sets of
    Periodic Orbits.” <i>Discrete and Continuous Dynamical Systems- Series A</i>.
    American Institute of Mathematical Sciences, 2024. <a href="https://doi.org/10.3934/dcds.2024059">https://doi.org/10.3934/dcds.2024059</a>.
  ieee: C. Fiorebe, “Examples of projective billiards with open sets of periodic orbits,”
    <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 44, no. 11. American
    Institute of Mathematical Sciences, pp. 3287–3301, 2024.
  ista: Fiorebe C. 2024. Examples of projective billiards with open sets of periodic
    orbits. Discrete and Continuous Dynamical Systems- Series A. 44(11), 3287–3301.
  mla: Fiorebe, Corentin. “Examples of Projective Billiards with Open Sets of Periodic
    Orbits.” <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 44,
    no. 11, American Institute of Mathematical Sciences, 2024, pp. 3287–301, doi:<a
    href="https://doi.org/10.3934/dcds.2024059">10.3934/dcds.2024059</a>.
  short: C. Fiorebe, Discrete and Continuous Dynamical Systems- Series A 44 (2024)
    3287–3301.
corr_author: '1'
date_created: 2024-07-14T22:01:10Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-10-16T11:53:22Z
day: '01'
department:
- _id: VaKa
doi: 10.3934/dcds.2024059
external_id:
  isi:
  - '001230091000001'
intvolume: '        44'
isi: 1
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.3934/dcds.2024059
month: '11'
oa: 1
oa_version: Published Version
page: 3287-3301
publication: Discrete and Continuous Dynamical Systems- Series A
publication_identifier:
  eissn:
  - 1553-5231
  issn:
  - 1078-0947
publication_status: published
publisher: American Institute of Mathematical Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Examples of projective billiards with open sets of periodic orbits
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 44
year: '2024'
...
---
_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
arxiv: 1
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. <i>Arnold Mathematical Journal</i>. 2022;8:411-422.
    doi:<a href="https://doi.org/10.1007/s40598-022-00198-y">10.1007/s40598-022-00198-y</a>
  apa: 'Bialy, M., Fiorebe, C., Glutsyuk, A., Levi, M., Plakhov, A., &#38; Tabachnikov,
    S. (2022). Open problems on billiards and geometric optics. <i>Arnold Mathematical
    Journal</i>. Hybrid: Springer Nature. <a href="https://doi.org/10.1007/s40598-022-00198-y">https://doi.org/10.1007/s40598-022-00198-y</a>'
  chicago: Bialy, Misha, Corentin Fiorebe, Alexey Glutsyuk, Mark Levi, Alexander Plakhov,
    and Serge Tabachnikov. “Open Problems on Billiards and Geometric Optics.” <i>Arnold
    Mathematical Journal</i>. Springer Nature, 2022. <a href="https://doi.org/10.1007/s40598-022-00198-y">https://doi.org/10.1007/s40598-022-00198-y</a>.
  ieee: M. Bialy, C. Fiorebe, A. Glutsyuk, M. Levi, A. Plakhov, and S. Tabachnikov,
    “Open problems on billiards and geometric optics,” <i>Arnold Mathematical Journal</i>,
    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.” <i>Arnold
    Mathematical Journal</i>, vol. 8, Springer Nature, 2022, pp. 411–22, doi:<a href="https://doi.org/10.1007/s40598-022-00198-y">10.1007/s40598-022-00198-y</a>.
  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'
...