Chaotic n-dimensional euclidean and hyperbolic open billiards and chaotic spinning planar billiards
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol.7, no.2, pp.421-436, 2008 (SCI-Expanded, Scopus)
- 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.