The Birkhoff-Poritsky conjecture for centrally-symmetric billiard tables

DOI10.4007/annals.2022.196.1.2zbMath1505.37067arXiv2008.03566OpenAlexW3048024723WikidataQ113692550 ScholiaQ113692550MaRDI QIDQ2171414

Andrey E. Mironov, Misha Bialy

Publication date: 9 September 2022

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.03566

zbMATH Keywords

Birkhoff-Poritsky conjectureBirkhoff billiardintegrable billiard

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods (37J51) 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)

Related Items (6)

Resonance of ellipsoidal billiard trajectories and extremal rational functions ⋮ Centrally symmetric analytic plane domains are spectrally determined in this class ⋮ On differential equations of integrable billiard tables ⋮ On the fragility of periodic tori for families of symplectic twist maps ⋮ Open problems on billiards and geometric optics ⋮ Locally maximising orbits for the non-standard generating function of convex billiards and applications

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