Topological entropy on zero-dimensional spaces

Jozef Bobok; Ondřej Zindulka

Fundamenta Mathematicae (1999)

  • Volume: 162, Issue: 3, page 233-249
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Bobok, Jozef, and Zindulka, Ondřej. "Topological entropy on zero-dimensional spaces." Fundamenta Mathematicae 162.3 (1999): 233-249. <http://eudml.org/doc/212422>.

@article{Bobok1999,
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.},
author = {Bobok, Jozef, Zindulka, Ondřej},
journal = {Fundamenta Mathematicae},
keywords = {dynamical system; topological entropy; homeomorphism; zero-dimensional compact space},
language = {eng},
number = {3},
pages = {233-249},
title = {Topological entropy on zero-dimensional spaces},
url = {http://eudml.org/doc/212422},
volume = {162},
year = {1999},
}

TY - JOUR
AU - Bobok, Jozef
AU - Zindulka, Ondřej
TI - Topological entropy on zero-dimensional spaces
JO - Fundamenta Mathematicae
PY - 1999
VL - 162
IS - 3
SP - 233
EP - 249
AB - 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.
LA - eng
KW - dynamical system; topological entropy; homeomorphism; zero-dimensional compact space
UR - http://eudml.org/doc/212422
ER -

References

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  1. [1] L. Alsedà, J. Llibre, and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One, Adv. Ser. Nonlinear Dynam. 5, World Sci., Singapore, 1993. Zbl0843.58034
  2. [2] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414. Zbl0212.29201
  3. [3] H. Cook, Continua which admit only the identity mapping onto nondegenerate subcontinua, Fund. Math. 60 (1967), 241-249. Zbl0158.41503
  4. [4] M. Denker, C. Grillenberger, and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, 1976. Zbl0328.28008
  5. [5] R. Engelking, Dimension Theory, North-Holland, Amsterdam, 1978. 
  6. [6] R. Engelking, General Topology, Heldermann, Berlin, 1989. 
  7. [7] S. Mazurkiewicz et W. Sierpiński, Contribution à la topologie des ensembles dénombrables, Fund. Math. 1 (1920), 17-27. Zbl47.0176.01
  8. [8] P. Walters, An Introduction to Ergodic Theory, Grad. Texts in Math. 79, Springer, New York, 1981. 

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