ArticleOriginal scientific text

Title

Topological entropy on zero-dimensional spaces

Authors 1, 1

Affiliations

  1. Department of Mathematics, Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 166 29 Praha 6, Czech Republic

Abstract

Let X be an uncountable compact metrizable space of topological dimension zero. Given any a ∈[0,∞] there is a homeomorphism on X whose topological entropy is a.

Keywords

dynamical system, topological entropy, homeomorphism, zero-dimensional compact space

Bibliography

  1. L. Alsedà, J. Llibre, and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One, Adv. Ser. Nonlinear Dynam. 5, World Sci., Singapore, 1993.
  2. R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414.
  3. H. Cook, Continua which admit only the identity mapping onto nondegenerate subcontinua, Fund. Math. 60 (1967), 241-249.
  4. M. Denker, C. Grillenberger, and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, 1976.
  5. R. Engelking, Dimension Theory, North-Holland, Amsterdam, 1978.
  6. R. Engelking, General Topology, Heldermann, Berlin, 1989.
  7. S. Mazurkiewicz et W. Sierpiński, Contribution à la topologie des ensembles dénombrables, Fund. Math. 1 (1920), 17-27.
  8. P. Walters, An Introduction to Ergodic Theory, Grad. Texts in Math. 79, Springer, New York, 1981.
Pages:
233-249
Main language of publication
English
Received
1998-08-31
Accepted
1999-09-06
Published
1999
Exact and natural sciences