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The structure of dendrites constructed by pointwise P-expansive maps on the unit interval

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  • 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.
    Mathematics Subject Classification: Primary: 37E05, 54C05; Secondary: 54F50.


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