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One-particle and few-particle billiards

Lansel, Steven and Porter, Mason A. and Bunimovich, Leonid A. (2006) One-particle and few-particle billiards. Chaos, 16 (1). Art. No. 013129. ISSN 1054-1500. doi:10.1063/1.2147740.

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We study the dynamics of one-particle and few-particle billiard systems in containers of various shapes. In few-particle systems, the particles collide elastically both against the boundary and against each other. In the one-particle case, we investigate the formation and destruction of resonance islands in (generalized) mushroom billiards, which are a recently discovered class of Hamiltonian systems with mixed regular-chaotic dynamics. In the few-particle case, we compare the dynamics in container geometries whose counterpart one-particle billiards are integrable, chaotic, and mixed. One of our findings is that two-, three-, and four-particle billiards confined to containers with integrable one-particle counterparts inherit some integrals of motion and exhibit a regular partition of phase space into ergodic components of positive measure. Therefore, the shape of a container matters not only for noninteracting particles but also for interacting particles.

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Additional Information:Copyright © 2006 American Institute of Physics. Received 29 August 2005; accepted 3 November 2005; published online 30 March 2006. S.L. and M.A.P. acknowledge support provided by an NSF VIGRE grant awarded to the School of Mathematics at Georgia Tech. The work of L.A.B. and S.L. was partially supported by NSF Grant No. DMS 0140165. L.A.B. also acknowledges the support of the Humboldt Foundation, S.L. acknowledges funding from a Georgia Tech PURA award, and M.A.P. acknowledges support from the Gordon and Betty Moore Foundation through Caltech’s Center for the Physics of Information. We also thank Bill Casselman and Nir Davidson for useful conversations and the anonymous referee for suggestions that led to significant improvements in the paper.
Subject Keywords:nonlinear dynamical systems; chaos
Issue or Number:1
Record Number:CaltechAUTHORS:LANchaos06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4546
Deposited By: Lindsay Cleary
Deposited On:28 Aug 2006
Last Modified:08 Nov 2021 20:18

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