A survey on polynomial in momenta integrals for billiard problems

Misha Bialy; Andrey E. Mironov

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

A survey on polynomial in momenta integrals for billiard problems

Misha Bialy, Andrey E. Mironov

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Review article › peer-review

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 twosided magnetic billiards introduced by Kozlov and Polikarpov. This article is part of the theme issue 'Finite dimensional integrable systems: new trends and methods'.

Original language	English
Article number	20170418
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	376
Issue number	2131
DOIs	https://doi.org/10.1098/rsta.2017.0418
State	Published - 28 Oct 2018

Keywords

Birkhoff conjecture
Magnetic billiards
Polynomial integrals
Two-sided magnetic billiards

All Science Journal Classification (ASJC) codes

General Engineering
General Physics and Astronomy
General Mathematics

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

Cite this

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KW - Polynomial integrals

KW - Two-sided magnetic billiards

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VL - 376

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

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M1 - 20170418

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A survey on polynomial in momenta integrals for billiard problems

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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