When different norms lead to same billiard trajectories?

DOI10.1007/s40879-020-00405-0OpenAlexW3016520463MaRDI QIDQ2095609

Roman N. Karasev, Arseniy V. Akopyan

Publication date: 17 November 2022

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.12685

zbMATH Keywords

billiardsHamiltonian systemsFinsler geometry

Mathematics Subject Classification ID

Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40) 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)

Cites Work

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• Billiards in Finsler and Minkowski geometries
• Elementary approach to closed billiard trajectories in asymmetric normed spaces
• Incircular nets and confocal conics
• A Brunn-Minkowski Inequality for Symplectic Capacities of Convex Domains
• A note on billiard systems in Finsler plane with elliptic indicatrices