Bialy Misha, Mironov Andrey E
School of Mathematical Sciences, Tel Aviv University, Israel
Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, and Novosibirsk State University, Pirogova st 1, 630090, Novosibirsk, Russia.
Philos Trans A Math Phys Eng Sci. 2018 Sep 17;376(2131):20170418. doi: 10.1098/rsta.2017.0418.
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'.
在本文中，我们简要综述了关于常曲率曲面上可积台球的伯克霍夫猜想代数版本的近期成果。我们还讨论了可积磁台球。作为代数技术的一个新应用，我们研究了由科兹洛夫和波利卡尔波夫引入的双侧磁台球的多项式积分的存在性。本文是主题为“有限维可积系统：新趋势与方法”的一部分。
