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Almost-Topological Conjugacy

  • Bruce P. Kitchens
Chapter
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Part of the Universitext book series (UTX)

Abstract

In this chapter we investigate two equivalence relations between subshifts of finite type. The first is finite equivalence and the second is almost-topological conjugacy. These equivalence relations are weaker than topological conjugacy which we discussed in Chapter 2. They are meant to capture the “typical” behavior of points in a subshift of finite type.

Keywords

Transition Matrix Irreducible Component Finite Type Topological Entropy Transitive Point 
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.

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References

  1. [AGW]
    R. Adler L.W. Goodwyn and B. Weiss, Equivalence of Topological Markov Shifts, Israel Journal of Mathematics no. 27 (1977), 49–63.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [AM]
    R. Adler and B. Marcus, Topological Entropy and Equivalence of Dynamical Systems, Memoirs of the American Mathematical Society no. 219 (1979).Google Scholar
  3. [AW1]
    R. Adler and B. Weiss, Entropy, a Complete Metric Invariant for Automorphisms of the Torus, Proceedings of the National Academy of Sciences, USA no. 57 (1967), 1573–1576.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [AW2]
    R. Adler and B. Weiss, Similarity of Automorphisms of the Torus, Memoirs of the American Mathematical Society no. 98 (1970).Google Scholar
  5. [Ay2]
    J. Ashley, Bounded-to-1 Factors of an Aperiodic Shift of Finite Type Arel-to-1 Almost Everywhere Factors Also, Ergodic Theory and Dynamical Systems 10 (1990), 615–625.MathSciNetzbMATHGoogle Scholar
  6. [Be]
    K. Berg, On the Conjugacy Problem for K-systems, Ph.D Thesis, University of Minnesota, (1967).Google Scholar
  7. [Ko]
    A. Kolmogorov, A New Metric Invariant for Transient Dynamical Systems, Academiia Nauk SSSR, Doklady 119 (1958), 861–864. (Russian)MathSciNetzbMATHGoogle Scholar
  8. [Or]
    D. Ornstein, Bernoulli Shifts with the Same Entropy are Isomorphic, Advances in Mathematics no. 4 (1970), 337–352.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [P3]
    W. Parry, A Finitary Classification of Topological Markov Chains and Sofic Systems, Bulletin of the London Mathematical Society 9 (1977) 86–92.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [Ru]
    D.J. Rudolph, Fundamentals of Measurable Dynamics, Clarendon Press, 1990.Google Scholar
  11. [Si2]
    Y. Sinai, On the Concept of Entropy for a Dynamical System, Academiia Nauk SSSR, Doklady 124 (1959), 768–771. (Russian)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Bruce P. Kitchens
    • 1
  1. 1.Mathematical Sciences DepartmentIBM T.J. Watson Research CenterYorktown HeightsUSA

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