Elementary approach to closed billiard trajectories in asymmetric normed spaces
Metric Geometry
2016-08-24 v4 Dynamical Systems
Abstract
We apply the technique of K\'aroly 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.
Keywords
Cite
@article{arxiv.1401.0442,
title = {Elementary approach to closed billiard trajectories in asymmetric normed spaces},
author = {Arseniy V. Akopyan and Alexey M. Balitskiy and Roman N. Karasev and Anastasia Sharipova},
journal= {arXiv preprint arXiv:1401.0442},
year = {2016}
}
Comments
10 figures added. The title changed