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Topological entropy of transitive dendrite maps

Published online by Cambridge University Press:  14 November 2013

VLADIMÍR ŠPITALSKÝ
VLADIMÍR ŠPITALSKÝ*
Affiliation:
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia email [email protected]
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Abstract

We show that every dendrite $X$ satisfying the condition that no subtree of $X$ contains all free arcs admits a transitive, even exactly Devaney chaotic map with arbitrarily small entropy. This gives a partial answer to a question of Baldwin from 2001.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 4 , June 2015 , pp. 1289 - 1314
Copyright
© Cambridge University Press, 2013 

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