On polynomially integrable Birkhoff billiards on surfaces of constant curvature

DOI10.4171/JEMS/1027zbMath1466.37049arXiv1706.04030OpenAlexW3107359156MaRDI QIDQ2659451

Alexey A. Glutsyuk

Publication date: 26 March 2021

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.04030

zbMATH Keywords

billiardsurface of constant curvaturepolynomial integralsingularities of algebraic curvesalgebraic Birkhoff conjecturegeodesic billiard flow

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Singularities of curves, local rings (14H20) 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 (13)

On curves with the Poritsky property ⋮ The Birkhoff-Poritsky conjecture for centrally-symmetric billiard tables ⋮ Resonance of ellipsoidal billiard trajectories and extremal rational functions ⋮ On differential equations of integrable billiard tables ⋮ Projective integrable mechanical billiards ⋮ On the fragility of periodic tori for families of symplectic twist maps ⋮ Conformal transformations and integrable mechanical billiards ⋮ A survey on polynomial in momenta integrals for billiard problems ⋮ On the integrability of Birkhoff billiards ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards ⋮ Topology of Liouville foliations of integrable billiards on table-complexes ⋮ Inverse problems and rigidity questions in billiard dynamics

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