A homeomorphism h:X → X of a compactum X is expansive provided that for some fixed c > 0 and any distinct x, y ∈ X there exists an integer n, dependent only on x and y, such that d(hⁿ(x),hⁿ(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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-3-3,
author = {Christopher Mouron},
title = {The solenoids are the only circle-like continua that admit expansive homeomorphisms},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {237-264},
zbl = {1182.54046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-3-3}
}
Christopher Mouron. The solenoids are the only circle-like continua that admit expansive homeomorphisms. Fundamenta Mathematicae, Tome 205 (2009) pp. 237-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-3-3/