Global Dynamics of the Breathing Circle Billiard

• Zhenbang Cao ^[1] ; Haotong Ma ^[1] ; Xuegang Yu ^[1] ; Yi Tan ^[1] ; Ge Ren ^[1] ; Bo Qi ^[1]
  1. [1] University of Chinese Academy of Sciences

     University of Chinese Academy of Sciences

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
• Enlaces
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• Resumen

  • In this paper we consider a breathing circle billiard which is described as a particle that travels inside a time-dependent circular domain and elastically reflecting from the boundary. Between collisions the particle moves with a constant speed along straight lines connecting the collision points. We show that in high energy situation, the dynamics of the system can be studied by constructing an area-preserving monotone twist map. Under appropriate assumptions, it is proved that there exist infinitely many bounded complete orbits, and a large class of periodic and quasi-periodic orbits for the system. This gives a description of the global dynamical behavior of the system.

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