Topological entropy on zero-dimensional spaces

• Autorzy: Jozef Bobok , Ondřej Zindulka
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 54H20: Topological dynamics
• 54C70: Entropy

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 162
• Numer: 3
• Strony: 233-249

Daty

wydano

1999

otrzymano

1998-08-31

poprawiono

1999-09-06

Twórcy

autor

Jozef Bobok

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

autor

Ondřej Zindulka

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

Bibliografia

• [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.