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, cilt.7, sa.2, ss.421-436, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7 Sayı: 2
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1137/060654189
  • Dergi Adı: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.421-436
  • Anahtar Kelimeler: chaos, billiards, dissipative, friction, BALL
  • Anadolu Üniversitesi Adresli: Evet

Özet

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.