Jose S. C\'anovas
Distributional chaos on tree maps: the star case

Comment.Math.Univ.Carolinae 42,3 (2001) 583-590.

Abstract:Let $\Bbb X =\{z\in \Bbb C:z^n\in [0,1]\}$, $n\in \Bbb N$, and let $f:\Bbb X \rightarrow \Bbb X$ be a continuous map having the branching point fixed. We prove that $f$ is distributionally chaotic iff the topological entropy of $f$ is positive.

Keywords: distributional chaos, topological entropy, star maps
AMS Subject Classification: 37B40, 37E25, 37D45