Chaotic n -Dimensional Euclidean and Hyperbolic Open Billiards and Chaotic Spinning Planar Billiards

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 th...

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Bibliographic Details
Published in:SIAM journal on applied dynamical systems 2008-01, Vol.7 (2), p.421-436
Main Authors: Deniz, Ali, Kennedy, Judy, Koçak, Şahin, Ratiu, Andrei V., Üstün, Cevat, Yorke, James A.
Format: Article
Language:English
Subjects:
Applied mathematics
Billiards
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Summary: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.
ISSN:1536-0040
1536-0040
DOI:10.1137/060654189