Geodesic
The classification of circle-like continua that admit expansive homeomorphisms
Christopher Mouron1
1 Department of Mathematics and Computer Science Rhodes College Memphis, TN 38112, U.S.A.
Fundamenta Mathematicae, Tome 211 (2011) no. 2, pp. 101-133 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm211-2-1
Keywords: homeomorphism rightarrow compactum expansive provided fixed every neq there exists integer dependent only hbox shown solenoid admits expansive homeomorphism homeomorphic regular solenoid concluded circle like continuum admits expansive homeomorphism only homeomorphic regular solenoid

Christopher Mouron 1

1 Department of Mathematics and Computer Science Rhodes College Memphis, TN 38112, U.S.A. 
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Christopher Mouron. The classification of circle-like continua
 that admit expansive homeomorphisms. Fundamenta Mathematicae, Tome 211 (2011) no. 2, pp. 101-133. doi: 10.4064/fm211-2-1

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