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

Anatoly Katok, Keith Burns

Research output: Contribution to journalArticle

59 Citations (Scopus)

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 - Jan 1 1994

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Invariant Cone
Lyapunov functions
Bernoulli
Lyapunov Function
Cones
Geodesic Flow
Riemannian Metric
Ergodicity
Compact Manifold
Lyapunov Exponent
Contact
Family

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems. / Katok, Anatoly; Burns, Keith.

In: Ergodic Theory and Dynamical Systems, Vol. 14, No. 4, 01.01.1994, p. 757-785.

Research output: Contribution to journalArticle

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