Chaotic n-dimensional euclidean and hyperbolic open billiards and chaotic spinning planar billiards

DENİZ A., Kennedy J., Kocak S., RATİU A. V., Ustun C., Yorke J. A.

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol.7, no.2, pp.421-436, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 2
  • Publication Date: 2008
  • Doi Number: 10.1137/060654189
  • Journal Name: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.421-436
  • Keywords: chaos, billiards, dissipative, friction, BALL
  • Anadolu University Affiliated: Yes

Abstract

We propose a new method to handle the n-dimensional billiard problem in the exterior of a finite mutually disjoint union of convex ( but not necessarily strictly convex) smooth obstacles without eclipse in the Euclidean or hyperbolic n-space, and we prove that there exist trajectories visiting the obstacles in any given doubly infinite prescribed order ( with the obvious restriction of no consecutive repetition). As an interesting variant of planar billiards, we consider spinning obstacles and particles and prove that any forward sequence of obstacles has a trajectory that follows it.