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

Anatole Katok, Keith Burns

Research output: Contribution to journalArticle

61 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)757-785
Number of pages29
JournalErgodic Theory and Dynamical Systems
Volume14
Issue number4
DOIs
StatePublished - Dec 1994

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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