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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.
Qualitative Theory of Dynamical Systems – Springer Journals
Published: Dec 1, 2022
Keywords: Breathing circle billiard; Twist map; Aubry-Mather sets; Complete orbits
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