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Semi-focusing billiards: ergodicity

Published online by Cambridge University Press:  01 October 2008

LEONID A. BUNIMOVICH  and
GIANLUIGI DEL MAGNO
LEONID A. BUNIMOVICH
Affiliation:
ABC Math Program and School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA (email: [email protected])
GIANLUIGI DEL MAGNO
Affiliation:
Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany (email: [email protected])
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Abstract

In Bunimovich and Del Magno [Semi-focusing billiards: hyperbolicity. Comm. Math. Phys.262 (2006), 17–32], we proved that billiards in certain three-dimensional convex domains are hyperbolic. In this paper, we continue the study of these systems, and prove that they enjoy the Bernoulli property. This result answers affirmatively a long-standing question on the existence of ergodic billiards in convex domains in dimensions greater than two. Besides, it shows that the chaotic components of the first rigorously investigated three-dimensional billiards with mixed phase space (mushroom billiards), introduced in Bunimovich and Del Magno, are in fact Bernoulli.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 5 , October 2008 , pp. 1377 - 1417
Copyright
Copyright © 2008 Cambridge University Press

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