On fourth-degree polynomial integrals of the Birkhoff billiard

M. Bialy, A. E. Mironov

Research output: Contribution to journalArticlepeer-review

Abstract

We study the Birkhoff billiard in a convex domain with a smooth boundary γ. We show that if this dynamical system has an integral which is polynomial in velocities of degree 4 and is independent with the velocity norm, then γ is an ellipse.

Original languageEnglish
Pages (from-to)27-32
Number of pages6
JournalProceedings of the Steklov Institute of Mathematics
Volume295
Issue number1
DOIs
StatePublished - 1 Nov 2016

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