A survey on polynomial in momenta integrals for billiard problems-Reference-Cited by-同舟云学术

A survey on polynomial in momenta integrals for billiard problems

Published:2018-09-17 Issue:2131 Volume:376 Page:20170418
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Bialy Misha¹^ORCID,Mironov Andrey E.²

Affiliation:

1. School of Mathematical Sciences, Tel Aviv University, Israel

2. Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, and Novosibirsk State University, Pirogova st 1, 630090, Novosibirsk, Russia

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 two-sided magnetic billiards introduced by Kozlov and Polikarpov. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.

Funder

Israel Science Foundation

Laboratory of Topology and Dynamics, Novosibirsk State University

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2017.0418

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