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

Tatsuya  Arai

doi:10.3934/dcds.2016.36.43

Article Contents

2016, Volume 36, Issue 1: 43-61. Doi: 10.3934/dcds.2016.36.43

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

Tatsuya Arai^1,

1.
Research and Support Center on Higher Education, for the Hearing Impaired and Visually Impaired, Tsukuba University of Technology, Ibaraki 305-8520

Received: May 2014

Revised: March 2015

Published: May 2017

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Abstract

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:

Pointwise $P$-expansive map,
universal dendrite.

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

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References

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