Billiards in Finsler and Minkowski geometries

DOI10.1016/S0393-0440(01)00039-0zbMath1022.70009OpenAlexW2068993570MaRDI QIDQ1602419

Eugene Gutkin, Sergei Tabachnikov

Publication date: 23 June 2002

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

Full work available at URL: https://doi.org/10.1016/s0393-0440(01)00039-0

zbMATH Keywords

least action principleFinsler geometrycausticssymplectomorphismmean free pathFinsler billiard mapFinsler billiard reflection lawmirror equationorbit-to-orbit dualityplanar Minkowski billiard

Mathematics Subject Classification ID

Dynamical systems in classical and celestial mechanics (37N05) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40) Collision of rigid or pseudo-rigid bodies (70F35) Dynamical systems methods for problems in mechanics (70G60)

Related Items (18)

Minkowski Geometry—Some Concepts and Recent Developments ⋮ Integrable topological billiards and equivalent dynamical systems ⋮ Magnetic billiards: non-integrability for strong magnetic field; Gutkin type examples ⋮ A survey on polynomial in momenta integrals for billiard problems ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ Duality of caustics in Minkowski billiards ⋮ Counting periodic trajectories of Finsler billiards ⋮ Finsler spinoptics ⋮ The broken ray transform in \(n\) dimensions with flat reflecting boundary ⋮ Billiard dynamics: An updated survey with the emphasis on open problems ⋮ From symplectic measurements to the Mahler conjecture ⋮ Caustic-free regions for billiards on surfaces of constant curvature ⋮ Polynomial non-integrability of magnetic billiards on the sphere and the hyperbolic plane ⋮ Pseudo-Riemannian geodesics and billiards ⋮ Topological billiards, conservation laws and classification of trajectories ⋮ When different norms lead to same billiard trajectories? ⋮ Billiards in ellipses revisited ⋮ Shortest closed billiard orbits on convex tables

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