Markov Partitions

  • Michael Shub


Our last major result will be counting the periodic points in a hyperbolic set with local product structure; we will carry this out using the important technique of symbolic dynamics.


Zeta Function Periodic Point Global Stability Unstable Manifold Finite Type 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [10.1]
    Adler, R. and Weiss. B., Similarity of automorphisms of the torus, Mem. Amer. Math. Soc. 98 (1970).Google Scholar
  2. [10.2]
    Artin, M. and Mazur, B., On periodic points, Ann. of Math. 81 (1965), 82.Google Scholar
  3. [10.3]
    Bowen, R. Markov partitions and minimal sets for Axiom A diffeomorphisms, Amer. J. Math. 92 (1970), 907.Google Scholar
  4. [10.4]
    Bowen, R. and Landford, O. III. Zeta functions of restrictions of the shift map, in Global Analysis, Vol XIV (Proceedings of Symposia in Pure Mathematics), American Mathematical Society, Providence, R.I., 1970, p. 43.Google Scholar
  5. [10.5]
    Guckenheimer, J., Axiom A + no cycles ç 1 (t) rational, Bull. Amer. Math. Soc. 76 (1970), 592.MathSciNetMATHCrossRefGoogle Scholar
  6. [10.6]
    Franks, J. Morse inequalities for zeta functions, Ann. of Math. 102 (1975), 143.Google Scholar
  7. [10.7]
    Franks, J., A reduced zeta function for diffeomorphisms, Ann. of Math. 100 (1978).Google Scholar
  8. [10.8]
    Fried, D., Rationality for Isolated Expansive Sets, Preprint, 1983.Google Scholar
  9. [10.9]
    Manning, A., Axiom A diffeomorphisms have rational zeta functions, Bull. Amer. Math. Soc. 3 (1971), 215.MathSciNetMATHGoogle Scholar
  10. [10.10]
    Manning, A., There are no new Anosov diffeomorphisms on tori, Amer. J. Math. 96 (1974), 422.MathSciNetMATHCrossRefGoogle Scholar
  11. [10.11]
    Shub, M. and Williams, R., Entropy and stability, Topology 14 (1975), 329.MathSciNetMATHCrossRefGoogle Scholar
  12. [10.12]
    Sinai, J. Markov partitions and C diffeomorphisms, Functional Anal. Appl. 2 (1968), 64.Google Scholar
  13. [10.13]
    Sinai, J., Construction of Markov partitions, Functional Anal. Appl. 2 (1968), 70.MathSciNetCrossRefGoogle Scholar
  14. [10.14]
    Sinai, J., Gibbs measures in ergodic theory, Russian Math. Surveys 166 (1972), 21.MathSciNetCrossRefGoogle Scholar
  15. [10.15]
    Williams, R., The zeta function of an attractor, Conference on the Topology of Manifolds (Michigan State University, East Lansing, Michigan), PrindleWeber and Schmidt, Boston, Mass., 1968, p. 155.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Michael Shub
    • 1
  1. 1.Thomas J. Watson Research CenterIBMYorktown HeightsUSA

Personalised recommendations