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Minimality, transitivity, mixing and topological entropy on spaces with a free interval

Published online by Cambridge University Press:  21 August 2012

MATÚŠ DIRBÁK ,
ĽUBOMÍR SNOHA  and
VLADIMÍR ŠPITALSKÝ
MATÚŠ DIRBÁK
Affiliation:
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia (email: Matus.Dirbak@umb.sk, Lubomir.Snoha@umb.sk, Vladimir.Spitalsky@umb.sk)
ĽUBOMÍR SNOHA
Affiliation:
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia (email: Matus.Dirbak@umb.sk, Lubomir.Snoha@umb.sk, Vladimir.Spitalsky@umb.sk)
VLADIMÍR ŠPITALSKÝ
Affiliation:
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia (email: Matus.Dirbak@umb.sk, Lubomir.Snoha@umb.sk, Vladimir.Spitalsky@umb.sk)
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Abstract

We study dynamics of continuous maps on compact metrizable spaces containing a free interval (i.e. an open subset homeomorphic to an open interval). Special attention is paid to relationships between topological transitivity, weak and strong topological mixing, dense periodicity and topological entropy as well as to the topological structure of minimal sets. In particular, a trichotomy for minimal sets and a dichotomy for transitive maps are proved.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 6 , December 2013 , pp. 1786 - 1812
Copyright
Copyright © 2012 Cambridge University Press 

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