Rotation Sets of Billiards with N Obstacles on a Torus

Zainab Alsheekhhussain

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Abstract

For billiards with N obstacles on a torus, we study the behavior of specific kind of its trajectories, the so called admissible trajectories. Using the methods developed in Blokh et al. (Commun Math Phys 266:239–265, 2006), we prove that the 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.

Original languageEnglish
Pages (from-to)369-377
Number of pages9
JournalDifferential Equations and Dynamical Systems
Volume27
Issue number4
DOIs
Publication statusPublished - 1 Oct 2019

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