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Differential Equations and Dynamical Systems

, Volume 27, Issue 4, pp 369–377 | Cite as

Rotation Sets of Billiards with N Obstacles on a Torus

  • Zainab AlsheekhhussainEmail author
Original Research

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.

Keywords

Torus General rotation set Admissible rotation set Rotation vector 

Notes

Acknowledgments

Financial support by the Ministry of Higher Education in Saudi Arabia is gratefully acknowledged.

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2015

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of Western AustraliaPerthAustralia

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