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Transitive dendrite map with zero entropy

Published online by Cambridge University Press:  08 March 2016

JAKUB BYSZEWSKI ,
FRYDERYK FALNIOWSKI  and
DOMINIK KWIETNIAK Open the ORCID record for DOMINIK KWIETNIAK [Opens in a new window]
JAKUB BYSZEWSKI
Affiliation:
Institute of Mathematics, Faculty of Mathematics and Computer Science, Łojasiewicza 6, 30-348 Kraków, Poland email [email protected]
FRYDERYK FALNIOWSKI
Affiliation:
Department of Mathematics, Cracow University of Economics, Rakowicka 27, 31-510 Kraków, Poland email [email protected]
DOMINIK KWIETNIAK
Affiliation:
Institute of Mathematics, Faculty of Mathematics and Computer Science, Łojasiewicza 6, 30-348 Kraków, Poland email [email protected] Institute of Mathematics, Federal University of Rio de Janeiro, Cidade Universitaria – Ilha do Fundão, Rio de Janeiro 21945-909, Brazil email [email protected]
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Abstract

Hoehn and Mouron [Hierarchies of chaotic maps on continua. Ergod. Th. & Dynam. Sys.34 (2014), 1897–1913] constructed a map on the universal dendrite that is topologically weakly mixing but not mixing. We modify the Hoehn–Mouron example to show that there exists a transitive (even weakly mixing) dendrite map with zero topological entropy. This answers the question of Baldwin [Entropy estimates for transitive maps on trees. Topology40(3) (2001), 551–569].

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 7 , October 2017 , pp. 2077 - 2083
Copyright
© Cambridge University Press, 2016 

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