TY - JOUR
T1 - A survey on polynomial in momenta integrals for billiard problems
AU - Bialy, Misha
AU - Mironov, Andrey E.
N1 - Publisher Copyright:
© 2018 The Author(s) Published by the Royal Society. All rights reserved.
PY - 2018/10/28
Y1 - 2018/10/28
N2 - 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'.
AB - 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'.
KW - Birkhoff conjecture
KW - Magnetic billiards
KW - Polynomial integrals
KW - Two-sided magnetic billiards
UR - http://www.scopus.com/inward/record.url?scp=85054130053&partnerID=8YFLogxK
U2 - 10.1098/rsta.2017.0418
DO - 10.1098/rsta.2017.0418
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AN - SCOPUS:85054130053
SN - 1364-503X
VL - 376
JO - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
JF - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
IS - 2131
M1 - 20170418
ER -