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

Anatole Katok, Keith Burns

Research output: Contribution to journalArticlepeer-review

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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