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Mean dimension, small entropy factors and an embedding theorem

  • Elon Lindenstrauss
Article

Abstract

In this paper we show how the notion of mean dimension is connected in a natural way to the following two questions: what points in a dynamical system (X, T) can be distinguished by factors with arbitrarily small topological entropy, and when can a system (X, T) be embedded in (([0, 1] d ) Z , shift). Our results apply to extensions of minimalZ-actions, and for this case we also show that there is a very satisfying dimension theory for mean dimension.

Keywords

Periodic Point Open Cover Topological Entropy Inverse Limit Minimal System 
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. [1]
    J. Auslander,Minimal flows and their extensions, Amsterdam, North-Holland (1988).zbMATHGoogle Scholar
  2. [2]
    W. Hurewicz andH. Wallman,Dimension Theory, Princeton University Press (1941).Google Scholar
  3. [3]
    A. Jaworski,University of Maryland Ph.D. Thesis (1974).Google Scholar
  4. [4]
    S. Kakutani, A proof of Bebutov’s theorem,J. of Differential Eq. 4 (1968), 194–201.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    E. Lindenstrauss, Lowering Topological Entropy,J. d’Analyse Math. 67 (1995), 231–267.MathSciNetGoogle Scholar
  6. [6]
    E. Lindenstrauss andB. Weiss, On Mean Dimension, to appear inIsrael J. of Math. Google Scholar
  7. [7]
    M. Shub andB. Weiss, Can one always lower topological entropy?,Ergod. Th. & Dynam. Sys. 11 (1991), 535–546.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Publications Mathematiques de L’I.H.E.S. 1999

Authors and Affiliations

  • Elon Lindenstrauss
    • 1
  1. 1.Institute of Mathematicsthe Hebrew UniversityJerusalemIsrael

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