Tree-like continua do not admit expansive homeomorphisms
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- by Christopher Mouron PDF
- Proc. Amer. Math. Soc. 130 (2002), 3409-3413 Request permission
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.References
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Additional Information
- Christopher Mouron
- Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
- Email: mouron@math.udel.edu
- Received by editor(s): August 16, 2000
- Received by editor(s) in revised form: June 21, 2001
- Published electronically: 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 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3409-3413
- MSC (2000): Primary 54H20, 54F50; Secondary 54E40
- DOI: https://doi.org/10.1090/S0002-9939-02-06447-X
- MathSciNet review: 1913021