DCDS
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
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.
DCDS
The structure of dendrites constructed by pointwise P-expansive maps on the unit interval
Tatsuya Arai
Let $f$ be a continuous map from the unit interval to itself. In this paper, we investigate the structure of space $Z$ which is constructed corresponding to the behaviors of $f$ and a periodic orbit $P$ of $f$. Under some restriction of $f$, we get necessary and sufficient conditions for $Z$ being the universal dendrite. Furthermore $Z$ is classified into five types especially when it is a tree.
keywords: universal dendrite. Pointwise $P$-expansive map

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