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

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Let f: X → X 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: I → I 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
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 3 , June 1995 , pp. 459 - 461
Copyright
Copyright © Australian Mathematical Society 1995

References

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