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Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems

Published online by Cambridge University Press:  19 September 2008

Anatole Katok  and
Keith Burns
Anatole Katok
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
Keith Burns
Affiliation:
Department of Mathematics, Northwestern University, Evanston, IL 60208, USA
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Abstract

We establish general criteria for ergodicity and Bernoulliness for volume preserving diffeormorphisms and flows on compact manifolds. We prove that every ergodic component with non-zero Lyapunov exponents of a contact flow is Bernoulli. As an application of our general results, we construct on every compact 3-dimensional manifold a C∞ Riemannian metric whose geodesic flow is Bernoulli.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 4 , December 1994 , pp. 757 - 785
Copyright
Copyright © Cambridge University Press 1994

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