---
_id: '8419'
abstract:
- lang: eng
  text: "In this survey, we provide a concise introduction to convex billiards and
    describe some recent results, obtained by the authors and collaborators, on the
    classification of integrable billiards, namely the so-called Birkhoff conjecture.\r\n\r\nThis
    article is part of the theme issue ‘Finite dimensional integrable systems: new
    trends and methods’."
article_number: '20170419'
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
- first_name: Alfonso
  full_name: Sorrentino, Alfonso
  last_name: Sorrentino
citation:
  ama: 'Kaloshin V, Sorrentino A. On the integrability of Birkhoff billiards. <i>Philosophical
    Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>.
    2018;376(2131). doi:<a href="https://doi.org/10.1098/rsta.2017.0419">10.1098/rsta.2017.0419</a>'
  apa: 'Kaloshin, V., &#38; Sorrentino, A. (2018). On the integrability of Birkhoff
    billiards. <i>Philosophical Transactions of the Royal Society A: Mathematical,
    Physical and Engineering Sciences</i>. The Royal Society. <a href="https://doi.org/10.1098/rsta.2017.0419">https://doi.org/10.1098/rsta.2017.0419</a>'
  chicago: 'Kaloshin, Vadim, and Alfonso Sorrentino. “On the Integrability of Birkhoff
    Billiards.” <i>Philosophical Transactions of the Royal Society A: Mathematical,
    Physical and Engineering Sciences</i>. The Royal Society, 2018. <a href="https://doi.org/10.1098/rsta.2017.0419">https://doi.org/10.1098/rsta.2017.0419</a>.'
  ieee: 'V. Kaloshin and A. Sorrentino, “On the integrability of Birkhoff billiards,”
    <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and
    Engineering Sciences</i>, vol. 376, no. 2131. The Royal Society, 2018.'
  ista: 'Kaloshin V, Sorrentino A. 2018. On the integrability of Birkhoff billiards.
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and
    Engineering Sciences. 376(2131), 20170419.'
  mla: 'Kaloshin, Vadim, and Alfonso Sorrentino. “On the Integrability of Birkhoff
    Billiards.” <i>Philosophical Transactions of the Royal Society A: Mathematical,
    Physical and Engineering Sciences</i>, vol. 376, no. 2131, 20170419, The Royal
    Society, 2018, doi:<a href="https://doi.org/10.1098/rsta.2017.0419">10.1098/rsta.2017.0419</a>.'
  short: 'V. Kaloshin, A. Sorrentino, Philosophical Transactions of the Royal Society
    A: Mathematical, Physical and Engineering Sciences 376 (2018).'
date_created: 2020-09-17T10:42:01Z
date_published: 2018-10-28T00:00:00Z
date_updated: 2021-01-12T08:19:09Z
day: '28'
doi: 10.1098/rsta.2017.0419
extern: '1'
intvolume: '       376'
issue: '2131'
keyword:
- General Engineering
- General Physics and Astronomy
- General Mathematics
language:
- iso: eng
month: '10'
oa_version: None
publication: 'Philosophical Transactions of the Royal Society A: Mathematical, Physical
  and Engineering Sciences'
publication_identifier:
  issn:
  - 1364-503X
  - 1471-2962
publication_status: published
publisher: The Royal Society
quality_controlled: '1'
status: public
title: On the integrability of Birkhoff billiards
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 376
year: '2018'
...