Angular billiard and algebraic Birkhoff conjecture

Misha Bialy, Andrey E. Mironov

Research output: Contribution to journalArticlepeer-review


In this paper we introduce a new dynamical system which we call Angular billiard. It acts on the exterior points of a convex curve in Euclidean plane. In a neighborhood of the boundary curve this system turns out to be dual to the Birkhoff billiard. Using this system we get new results on algebraic Birkhoff conjecture on integrable billiards.

Original languageEnglish
Pages (from-to)102-126
Number of pages25
JournalAdvances in Mathematics
StatePublished - 20 Jun 2017


  • Birkhoff billiards
  • Birkhoff conjecture
  • Polynomial integrals


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