On two-dimensional polynomially integrable billiards on surfaces of constant curvature

DOI10.1134/S1064562418050253zbMath1400.37063OpenAlexW2891407370WikidataQ126049540 ScholiaQ126049540MaRDI QIDQ1994099

Yanyan Li

Publication date: 1 November 2018

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562418050253

zbMATH Keywords

surface of constant curvatureBirkhoff conjecturealgebraic-geometric problem

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30)

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Cites Work

• Unnamed Item
• An integrable deformation of an ellipse of small eccentricity is an ellipse
• On fourth-degree polynomial integrals of the Birkhoff billiard
• Angular billiard and algebraic Birkhoff conjecture
• Integrable Birkhoff billiards
• Confocal surfaces and integrable billiards on the sphere and in the Lobachevsky space
• Integrable discrete-time systems and difference operators
• On algebraically integrable outer billiards
• Integrable billiards
• Integrable billiards on surfaces of constant curvature
• On the local Birkhoff conjecture for convex billiards
• On integrable systems with elastic reflections
• Algebraic Birkhoff conjecture for billiards on sphere and hyperbolic plane