A survey on polynomial in momenta integrals for billiard problems

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...

Full description

Saved in:
Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2018-09, Vol.376 (2131), p.20170418
Main Authors: Bialy, Misha, Mironov, Andrey E.
Format: Article
Language:English
Subjects:
Birkhoff Conjecture
Magnetic Billiards
Polynomial Integrals
Two-Sided Magneticbilliards
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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'.
ISSN:1364-503X
1471-2962
DOI:10.1098/rsta.2017.0418