Integrable billiards on surfaces of constant curvature

DOI10.1007/BF02102114zbMath0795.58028MaRDI QIDQ1311064

Sergey V. Bolotin

Publication date: 8 February 1994

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

geodesicsalgebraic curvesBirkhoff integrability

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Ordinary differential equations and systems on manifolds (34C40) Algebraic functions and function fields in algebraic geometry (14H05) Multiobjective variational problems, Pareto optimality, applications to economics, etc. (58E17)

Related Items (15)

Convex billiards on convex spheres ⋮ Periodic orbits of oval billiards on surfaces of constant curvature ⋮ Virtual billiards in pseudo-Euclidean spaces: discrete Hamiltonian and contact integrability ⋮ On a conjugacy problem in billiard dynamics ⋮ On polynomially integrable planar outer billiards and curves with symmetry property ⋮ Algebraic Birkhoff conjecture for billiards on sphere and hyperbolic plane ⋮ On polynomially integrable Birkhoff billiards on surfaces of constant curvature ⋮ On commuting billiards in higher-dimensional spaces of constant curvature ⋮ Resonance of ellipsoidal billiard trajectories and extremal rational functions ⋮ On differential equations of integrable billiard tables ⋮ Billiard map and rigid rotation ⋮ A survey on polynomial in momenta integrals for billiard problems ⋮ On two-dimensional polynomially integrable billiards on surfaces of constant curvature ⋮ Polynomial non-integrability of magnetic billiards on the sphere and the hyperbolic plane ⋮ Billiards on constant curvature spaces and generating functions for systems with constraints

Cites Work

• Poisson manifolds and the Schouten bracket
• First integrals of systems with elastic reflections
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Integrable billiards on surfaces of constant curvature