Advertisement

Symbolic dynamics for hyperbolic systems

  • Rufus Bowen
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 318)

Keywords

Periodic Orbit Zeta Function Periodic Point Finite Type Topological Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. L. Adler and B. Weiss. Entropy, a complete metric invariant for automorphisms of the torus, Proc. Natl. Acad. Sci. 57Google Scholar
  2. 2.
    R. Bowen. Markov partitions for Axiom A diffeomorphisms, Amer. J. Math. 92 (1970), 725–747.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    _____. Markov partitions and minimal sets for Axiom A diffeomorphisms, Amer. J. Math. 94 (1970), 907–918.MathSciNetCrossRefGoogle Scholar
  4. 4.
    _____. Periodic orbits for hyperbolic flows, Amer. J. Math.Google Scholar
  5. 5.
    _____. One-dimensional hyperbolic sets for flows, Jour. Diff. Eqns.Google Scholar
  6. 6.
    _____. Periodic points and measures for Axiom A diffeomorphisms, Trans. Amer. Math. Soc. 154 (1971), 377–397.MathSciNetzbMATHGoogle Scholar
  7. 7.
    _____. Maximizing entropy for a hyperbolic flow, Math. Systems Theory.Google Scholar
  8. 8.
    R. Bowen and O. E. Lanford. Zeta functions of restrictions of the shift transformation, Proc. Symp. Pure Math., Vol. 14 (1970), 43–49.MathSciNetCrossRefGoogle Scholar
  9. 9.
    L. W. Goodwyn. Topological entropy bounds measure theoretic entropy, Proc. Amer. Math. Soc. 23 (1969), 679–688.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    J. Guckenheimer. Axiom A and nocycles imply ζ f (t) rational, Bull. Amer. Math. Soc. 76 (1970), 592–594.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    J. Hadamard. Les surfaces a courbures opposees e leur liques geodesiques, Jr. Math. Pures Appl. 4 (1898), 27–73.Google Scholar
  12. 12.
    G. A. Hedlund. Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory, 3 (1969), 320–375.MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    G. A. Hedlund and M. Morse. Symbolic dynamics, Amer. J. Math. 69 (1938), 815–866.MathSciNetGoogle Scholar
  14. 14.
    A. Manning. Axiom A diffeomorphisms have rational zeta functions, functions, Bull. London Math. Soc. 3 (1971), 215–220.MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    M. Morse. Representation of geodesics, Amer. J. Math. 43 (1921), 33–51.MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    _____. Recurrent geodesics on a surface of negative curvature, Trans. Amer. Math. Soc. 22 (1921), 84–110.MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    _____. Symbolic dynamics, lecture notes, Institute for Advanced Study, Princeton.Google Scholar
  18. 18.
    N. Friedman and D. Ornstein, On isomorphism of weak Bernoulli transformations, Advances in Math. 5(1970), 365–394.MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    W. Parry. Intrinsic Markov chains, Trans. Amer. Math. Soc. 112 (1964), 55–66.MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Ya. G. Sinai. Markov partitions and C-diffeomorphisms, Func. Anal. and its Appl. 2 (1968), no. 1, 64–89.MathSciNetGoogle Scholar
  21. 21.
    S. Smale. Diffeomorphisms with many periodic points, "Differential and Combinatorial Topology", Princeton 1965, 63–80.Google Scholar
  22. 22.
    _____. Differentiable Dynamical Systems, Bull. Amer. Math. Soc. 73 (1967), 747–817.MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    R. Bowen. Topological entropy and Axiom A, Proc. Symp. Pure Math., Vol. 14 (1970), 23–41.MathSciNetCrossRefGoogle Scholar
  24. 24.
    _____. Symbolic dynamics for hyperbolic flows, Amer. J. Math.Google Scholar
  25. 25.
    D. Ruelle, Statistical mechanics on a compact set with Z v action satisfying expansiveness and specification.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Rufus Bowen
    • 1
  1. 1.University of CaliforniaBerkeley

Personalised recommendations