A survey on Polynomial in momenta integrals for billiard problems

2018/04/05 by Michael Michael, Michael, Bialy +2 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1804.01686

openalex publication_date 2018/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

In this paper we give a short survey of recent results on 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.

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• On complex algebraic caustics in planar and projective billiards

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