On differential equations of integrable billiard tables

DOI10.1007/S10114-024-2450-5arXiv2207.09585MaRDI QIDQ6139294

Vladimir Dragović, Andrey E. Mironov

Publication date: 18 January 2024

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.09585

zbMATH Keywords

polynomial first integralspiecewise smooth surfaceswire billiards

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39) Dynamical systems with singularities (billiards, etc.) (37C83)

Cites Work

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• On the local Birkhoff conjecture for convex billiards
• The Birkhoff-Poritsky conjecture for centrally-symmetric billiard tables
• Wire billiards, the first steps
• On polynomially integrable Birkhoff billiards on surfaces of constant curvature
• Poncelet Porisms and Beyond
• On Local Integrability in Billiard Dynamics

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