Rotation Sets of Billiards with N Obstacles on a Torus
Dynamical Systems
2016-03-14 v1
Abstract
For billiards with obstacles on a torus, we study the behavior of specific kind of its trajectories, \emph{the so called admissible trajectories}. Using the methods developed in \cite{1}, we prove that the \emph{admissible rotation set} is convex, and the periodic trajectories of admissible type are dense in the admissible rotation set. In addition, we show that the admissible rotation set is a proper subset of the general rotation set.
Keywords
Cite
@article{arxiv.1603.03527,
title = {Rotation Sets of Billiards with N Obstacles on a Torus},
author = {Zainab Alsheekhhussain},
journal= {arXiv preprint arXiv:1603.03527},
year = {2016}
}
Comments
12 pAGES, Rotation sets of billiards with N obstacles on a torus, Differ. Equ. Dyn. Syst. (2015)