A survey on polynomial in momenta integrals for billiard problems

Misha Bialy, Andrey E. Mironov

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In this paper, we give a short survey of recent results on the algebraic version of the Birkhoff conjecture for integrable billiards on surfaces of constant curvature. We also discuss integrable magnetic billiards. As a new application of the algebraic technique, we study the existence of polynomial integrals for the twosided magnetic billiards introduced by Kozlov and Polikarpov. This article is part of the theme issue 'Finite dimensional integrable systems: new trends and methods'.

Original languageEnglish
Article number20170418
Number of pages19
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume376
Issue number2131
DOIs
Publication statusPublished - 17 Sep 2018

Keywords

  • Birkhoff conjecture
  • Magnetic billiards
  • Polynomial integrals
  • Two-sided magnetic billiards
  • FIELDS
  • polynomial integrals
  • CONVEX BILLIARDS
  • MAGNETIC BILLIARDS
  • CLASSICAL BILLIARDS
  • BIRKHOFF CONJECTURE
  • CONSTANT CURVATURE
  • magnetic billiards
  • two-sided magnetic billiards
  • SURFACES

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