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Pointwise-recurrent dendrite maps

Published online by Cambridge University Press:  09 July 2012

ISSAM NAGHMOUCHI
ISSAM NAGHMOUCHI*
Affiliation:
Department of Mathematics, Faculty of Sciences of Bizerte, University of Carthage, Jarzouna, 7021, Tunisia (email: [email protected])
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Abstract

Let $D$ be a dendrite and $f:D\rightarrow D$ a continuous map. Denote by $E(D)$ and $B(D)$ the sets of endpoints and branch points of $D$, respectively. We show that if $E(D)$ is countable, then $f$ is pointwise-recurrent if and only if $f$ is a pointwise-periodic homeomorphism; also, if $B(D)$ is discrete, then $f$ is pointwise-recurrent if and only if every point in $D\backslash E(D)$is periodic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 4 , August 2013 , pp. 1115 - 1123
Copyright
Copyright © 2012 Cambridge University Press 

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