Hereditarily indecomposable compacta do not admit expansive homeomorphisms

Kato, Hisao; Mouron, Christopher

doi:10.1090/S0002-9939-08-09316-7

Hereditarily indecomposable compacta do not admit expansive homeomorphisms
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by Hisao Kato and Christopher G. Mouron PDF

Proc. Amer. Math. Soc. 136 (2008), 3689-3696 Request permission

Abstract:

A homeomorphism $h:X\longrightarrow X$ is 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 $\mbox {d}(h^n(x),h^n(y))>c$. It is shown that if $X$ is a hereditarily indecomposable compactum, then $h$ cannot be expansive.

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