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Nonuniformly hyperbolic K-systems are Bernoulli

Published online by Cambridge University Press:  19 September 2008

N. I. Chernov  and
C. Haskell
N. I. Chernov
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA
C. Haskell
Affiliation:
State University of New York at Stony Brook, Stony Brook, New York 11794-3660, USA
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Abstract

We prove that those non-uniformly hyperbolic maps and flows (with singularities) that enjoy the K-property are also Bernoulli. In particular, many billiard systems, including those systems of hard balls and stadia that have the K-property, and hyperbolic billiards, such as the Lorentz gas in any dimension, are Bernoulli. We obtain the Bernoulli property for both the billiard flows and the associated maps on the boundary of the phase space.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 1 , February 1996 , pp. 19 - 44
Copyright
Copyright © Cambridge University Press 1996

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