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Global Dynamics of the Breathing Circle Billiard

Global Dynamics of the Breathing Circle Billiard 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Qualitative Theory of Dynamical Systems Springer Journals

Global Dynamics of the Breathing Circle Billiard

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References (36)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022
ISSN
1575-5460
eISSN
1662-3592
DOI
10.1007/s12346-022-00619-5
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Qualitative Theory of Dynamical SystemsSpringer Journals

Published: Dec 1, 2022

Keywords: Breathing circle billiard; Twist map; Aubry-Mather sets; Complete orbits

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