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Tree-like continua do not admit expansive homeomorphisms

Author(s): Christopher Mouron
Journal: Proc. Amer. Math. Soc. 130 (2002), 3409-3413.
MSC (2000): Primary 54H20, 54F50; Secondary 54E40
Posted: May 14, 2002
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Abstract: A homeomorphism $h:X \rightarrow X$ is called expansive provided that for some fixed $c >0$ and every $x,y \in X$ there exists an integer $n$, dependent only on $x$ and $y$, such that $d(h^n(x),h^n(y))>c$. It is shown that if $X$ is a tree-like continuum, then $h$ cannot be expansive.

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H. Kato, Continuum-wise expansive homeomorphisms, Can. J. Math. 45(1993), no. 3, 576-598. MR 94k:54065

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Additional Information:

Christopher Mouron
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
Email: mouron@math.udel.edu

DOI: 10.1090/S0002-9939-02-06447-X
PII: S 0002-9939(02)06447-X
Keywords: Expansive homeomorphism, tree-like continua
Received by editor(s): August 16, 2000
Received by editor(s) in revised form: June 21, 2001
Posted: May 14, 2002
Additional Notes: The author is pleased to acknowledge the many useful comments and suggestions made by Charles Hagopian
Communicated by: Alan Dow
Copyright of article: Copyright 2002, American Mathematical Society

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