A survey on polynomial in momenta integrals for billiard problems

Misha Bialy*, Andrey E. Mironov

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review


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
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2131
StatePublished - 28 Oct 2018


  • Birkhoff conjecture
  • Magnetic billiards
  • Polynomial integrals
  • Two-sided magnetic billiards


Dive into the research topics of 'A survey on polynomial in momenta integrals for billiard problems'. Together they form a unique fingerprint.

Cite this