Elementary approach to closed billiard trajectories in asymmetric normed spaces
Copyright policy )Elementary approach to closed billiard trajectories in asymmetric normed spaces
We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a lower bound for the length of the shortest closed billiard trajectory, related to the non-symmetric Mahler problem. With this technique we are able to give short and elementary proofs to some known results.
- Institute for Information Transmission Problems Russian Federation
- Institute of Science and Technology Austria Austria
- Moscow Institute of Physics and Technology Russian Federation
- Moscow Institute of Physics and Technology Russian Federation
Metric Geometry (math.MG), Dynamical Systems (math.DS), Minkowski norm, Mahler's conjecture, Convex sets in \(n\) dimensions (including convex hypersurfaces), Global theory of symplectic and contact manifolds, Mathematics - Metric Geometry, Minkowski billiard, 52A20, 52A23, 53D35, Asymptotic theory of convex bodies, FOS: Mathematics, billiards, Mathematics - Dynamical Systems
Metric Geometry (math.MG), Dynamical Systems (math.DS), Minkowski norm, Mahler's conjecture, Convex sets in \(n\) dimensions (including convex hypersurfaces), Global theory of symplectic and contact manifolds, Mathematics - Metric Geometry, Minkowski billiard, 52A20, 52A23, 53D35, Asymptotic theory of convex bodies, FOS: Mathematics, billiards, Mathematics - Dynamical Systems
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