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Transitive dendrite map with zero entropy
Published online by Cambridge University Press: 08 March 2016
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].
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- © Cambridge University Press, 2016
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