Transitive dendrite map with zero entropy

Abstract

Hoehn and Mouron [Ergod. Th. \& Dynam. Sys. (2014) \textbf{34}, 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 [Topology (2001) \textbf{40}, 551--569].