Geodesic
Distributional chaos on tree maps: the star case
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 3, pp. 583-590 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 37B40, 37D45, 37E25, 54H20
Keywords: distributional chaos; topological entropy; star maps 
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     author = {C\'anovas, Jose S.},
     title = {Distributional chaos on tree maps: the star case},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {583--590},
     year = {2001},
     volume = {42},
     number = {3},
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     zbl = {1052.37032},
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Cánovas, Jose S. Distributional chaos on tree maps: the star case. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 3, pp. 583-590. http://geodesic.mathdoc.fr/item/CMUC_2001_42_3_a16/