The classification of circle-like continua that admit expansive homeomorphisms
Volume 211 / 2011
Fundamenta Mathematicae 211 (2011), 101-133
MSC: Primary 37B45; Secondary 54F15.
DOI: 10.4064/fm211-2-1
Abstract
A homeomorphism $h:X\rightarrow X$ of a compactum $X$ is expansive provided that for some fixed $c>0$ and every $x, y\in X\ (x\neq y)$ there exists an integer $n$, dependent only on $x$ and $y$, such that $\hbox{d}(h^n(x),h^n(y))>c$. It is shown that if $X$ is a solenoid that admits an expansive homeomorphism, then $X$ is homeomorphic to a regular solenoid. It can then be concluded that a circle-like continuum admits an expansive homeomorphism if and only if it is homeomorphic to a regular solenoid.
