The construction of chaotic maps in the sense of Devaney on dendrites which commute to continuous maps on the unit interval
Tatsuya Arai Naotsugu Chinen
Discrete & Continuous Dynamical Systems - A 2004, 11(2&3): 547-556 doi: 10.3934/dcds.2004.11.547
Let $f$ be a continuous map from the unit interval to itself. In this paper, it is shown that $f$ has positive topological entropy if and only if $f$ is pointwise $P$-expansive for some periodic orbit $P$ of $f$. And it is also proved that if $f$ has a periodic orbit with odd period, then there exists a chaotic map from a dendrite to itself in the sense of Devaney which is semiconjugate to $f$ and has positive topological entropy.
keywords: Sharkovsky ordering topological entropy Chaotic map in the sense of Devaney pointwise P-expansive.

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