Skip to main content
SpringerLink
Log in

Smooth partitions of Anosov diffeomorphisms are weak Bernoulli

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

It is shown that smooth partitions are weak Bernoulli forC 2 measure preserving Anosov diffeomorphisms. A related type of coding is defined and an invariant discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Adler and B. Weiss,Similarity of automorphisms of the torus, Mem. Amer. Math. Soc.98 (1970).

  2. D. Anosov,Geodesic flows on closed Riemann manifolds with negative curvature, Proc. Steklov Inst. Math.90 (1967).

  3. R. Azencott,Difféomorphismes d’Anosov et schémas de Bernoulli, C. R. Acad. Sci. Paris Sér. A-B270, A1105-A1107 (1970).

    MathSciNet  Google Scholar 

  4. N. Friedman and D. S. Ornstein,An isomorphism of weak Bernoulli transformations, Advances in Math.5 (1971), 365–394.

    Article  MathSciNet  Google Scholar 

  5. M. Ratner,The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature, Israel J. Math.16 (1973), 181–197.

    Article  MathSciNet  Google Scholar 

  6. D. Ruelle,A measure associated with Axiom A attractors, Amer. J. Math., to appear.

  7. Ya. Sinai,Markov partitions and C-diffeomorphisms, Functional Anal. Appl.2 (1968), 245–253.

    Article  Google Scholar 

  8. Ya. Sinai,Gibbs measures in ergodic theory, Russian Math. Surveys166 (1972), 21–69.

    Article  MathSciNet  Google Scholar 

  9. B. Weiss,The structure of Bernoulli systems, Int. Congr. Math. 1974.

  10. L. Meshalkin,A case of isomorphism of Bernoulli schemes, Dokl. Akad. Nauk SSSR128 (1959), 41–44.

    MATH  MathSciNet  Google Scholar 

  11. D. Ornstein,What does it mean for a mechanical system to be isomorphic to a Bernoulli flow?, to appear.

Download references

Authors
  1. Rufus Bowen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the Sloan Foundation and NSF GP-14519.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bowen, R. Smooth partitions of Anosov diffeomorphisms are weak Bernoulli. Israel J. Math. 21, 95–100 (1975). https://doi.org/10.1007/BF02760788

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02760788

Keywords

Search

Navigation