The solenoids are the only circle-like continua that admit expansive homeomorphisms
Volume 205 / 2009
Fundamenta Mathematicae 205 (2009), 237-264
MSC: Primary 54H20, 54F50; Secondary 54E40.
DOI: 10.4064/fm205-3-3
Abstract
A homeomorphism $h:X\rightarrow X$ of a compactum $X$ is expansive provided that for some fixed $c>0$ and any distinct $x, y\in X$ 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 circle-like continuum that admits an expansive homeomorphism, then $X$ is homeomorphic to a solenoid.
