Pseudo-Euclidean billiards within confocal curves on the hyperboloid of one sheet

DOI10.1016/j.geomphys.2020.104032zbMath1464.14036arXiv2008.06158OpenAlexW3049240348WikidataQ114173627 ScholiaQ114173627MaRDI QIDQ2223753

Milena Radnović, Sean Gasiorek

Publication date: 1 February 2021

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.06158

zbMATH Keywords

geodesicsMinkowski spacebilliardsperiodic trajectoriesconfocal quadricselliptic billiards

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relationships between algebraic curves and integrable systems (14H70) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39) Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions (37J38)

Related Items (1)

Geodesic scattering on hyperboloids and Knörrer’s map

Cites Work

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• Ellipsoidal billiards in pseudo-Euclidean spaces and relativistic quadrics
• Confocal surfaces and integrable billiards on the sphere and in the Lobachevsky space
• Pseudo-Riemannian geodesics and billiards
• Discrete versions of some classical integrable systems and factorization of matrix polynomials
• A Poncelet theorem in space
• On elliptical billiards in the Lobachevsky space and associated geodesic hierarchies.
• Geodesics on an ellipsoid in Minkowski space
• Minkowski plane, confocal conics, and billiards
• Confocal Conics in Space-Time
• Conditions of Cayley’s type for ellipsoidal billiard
• On periodical trajectories of the billiard systems within an ellipsoid in Rd and generalized Cayley’s condition
• Geometry. I, II. Transl. from the French by M. Cole and S. Levy

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