On fourth-degree polynomial integrals of the Birkhoff billiard

M. Bialy; A. E. Mironov

doi:10.1134/S0081543816080022

On fourth-degree polynomial integrals of the Birkhoff billiard

M. Bialy
, A. E. Mironov

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	27-32
Number of pages	6
Journal	Proceedings of the Steklov Institute of Mathematics
Volume	295
Issue number	1
DOIs	https://doi.org/10.1134/S0081543816080022
State	Published - 1 Nov 2016

ASJC Scopus subject areas

Mathematics (miscellaneous)

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title = "On fourth-degree polynomial integrals of the Birkhoff billiard",

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.",

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N2 - 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.

AB - 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.

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DO - 10.1134/S0081543816080022

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JO - Proceedings of the Steklov Institute of Mathematics

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On fourth-degree polynomial integrals of the Birkhoff billiard

Abstract

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