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Israel Journal of Mathematics

, Volume 115, Issue 1, pp 1–24 | Cite as

Mean topological dimension

  • Elon Lindenstrauss
  • Benjamin Weiss
Article

Abstract

In this paper we present some results and applications of a new invariant for dynamical systems that can be viewed as a dynamical analogue of topological dimension. This invariant has been introduced by M. Gromov, and enables one to assign a meaningful quantity to dynamical systems of infinite topological dimension and entropy. We also develop an alternative approach that is metric dependent and is intimately related to topological entropy.

Keywords

Topological Dimension Open Cover Finite Subset Amenable Group 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.

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References

  1. [1]
    J. Auslander,Minimal Flows and Their Extensions, Chapter 13, Amsterdam, North-Holland, 1988, pp. 183–194.zbMATHGoogle Scholar
  2. [2]
    S. Glasner and D. Maon,An inverted tower of almost 1-1 extensions, Journal d'Analyse Mathématique44 (1984/85), 67–75.MathSciNetGoogle Scholar
  3. [3]
    W. Hurewicz and H. Wallman,Dimension Theory, Princeton University Press, 1941.Google Scholar
  4. [4]
    A. Jaworski, Ph.D. thesis, University of Maryland, 1974.Google Scholar
  5. [5]
    S. Kakutani,A proof of Bebutov's theorem, Journal of Differential Equations4 (1968), 194–201.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    E. Lindenstrauss,Lowering topological entropy, Journal d'Analyse Mathématique67 (1995), 231–267.MathSciNetGoogle Scholar
  7. [7]
    E. Lindenstrauss,Mean dimension, small entropy factors and an imbedding theorem, preprint.Google Scholar
  8. [8]
    J. Ollagnier,Ergodic Theory and Statistical Mechanics, Lecture Notes in Mathematics1115, Springer-Verlag, Berlin, 1985.zbMATHGoogle Scholar
  9. [9]
    D. Ornstein and B. Weiss,Entropy and isomorphism theorems for actions of amenable groups, Journal d'Analyse Mathématique,48 (1987), 1–141.zbMATHMathSciNetGoogle Scholar
  10. [10]
    L. Pontryagin and L. Schnirelmann,Sur une propriété métrique de la dimension, Annals of Mathematics,II Ser. 33 (1932), 152–162.MathSciNetGoogle Scholar
  11. [11]
    M. Shub and B. Weiss,Can one always lower topological entropy?, Ergodic Theory and Dynamical Systems11 (1991), 535–546.zbMATHMathSciNetCrossRefGoogle Scholar
  12. [12]
    J. C. Kieffer,A ratio limit theorem for a strongly subadditive set function in a locally compact amenable group, Pacific Journal of Mathematics61 (1975), 183–190.zbMATHMathSciNetGoogle Scholar
  13. [13]
    W. R. Emerson,Averaging strongly subadditive set functions in unimodular amenable groups I, Pacific Journal of Mathematics61 (1975), 391–400.zbMATHMathSciNetGoogle Scholar

Copyright information

© Hebrew University 2000

Authors and Affiliations

  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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