Resumen de Global Dynamics of the Breathing Circle Billiard

Zhenbang Cao, Haotong Ma, Xuegang Yu, Yi Tan, Ge Ren, Bo Qi

• 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.