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A note on periodic points and recurrent points of maps of dendrites

Published online by Cambridge University Press:  17 April 2009

Hisao Kato
Affiliation:
Institute of Matehamtics, University of Tsukuba, Ibarald 305, Japan
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Abstract

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Let f: XX be a map of a continuum X. Let P(f) denote the set of all periodic points of f and R(f) denote the set of all recurrent points of f. In [2], Coven and Hedlund proved that if f: II is a map of the unit interval I = [0, 1], then CI(P(f)) = CI(R(f)). In [7], Ye generalised this result to maps of a tree. It is natural to ask whether the result generalises to maps of a dendrite. (A dendrite is a locally connected continuum which contains no simple closed curve.) The aim of this paper is to show that the answer is negative.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1995
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