Geodesic
The solenoids are the only 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 205 (2009) no. 3, pp. 237-264

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm205-3-3
Keywords: homeomorphism rightarrow compactum expansive provided fixed distinct there exists integer dependent only shown circle like continuum admits expansive homeomorphism homeomorphic 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 solenoids are the only circle-like
 continua that admit expansive homeomorphisms. Fundamenta Mathematicae, Tome 205 (2009) no. 3, pp. 237-264. doi: 10.4064/fm205-3-3

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