Tree-like continua do not admit expansive homeomorphisms

Mouron, Christopher

doi:10.1090/S0002-9939-02-06447-X

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.

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