The classification of circle-like continua that admit expansive homeomorphisms

Tom 211 / 2011

Christopher Mouron Fundamenta Mathematicae 211 (2011), 101-133 MSC: Primary 37B45; Secondary 54F15. DOI: 10.4064/fm211-2-1


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.


  • Christopher MouronDepartment of Mathematics and Computer Science
    Rhodes College
    Memphis, TN 38112, U.S.A.

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