A homeomorphism h: X → X of a compactum X is expansive provided that for some fixed c > 0 and every x, y ∈ X (x ≠ y) 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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-2-1,
author = {Christopher Mouron},
title = {The classification of circle-like continua that admit expansive homeomorphisms},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {101-133},
zbl = {1218.37023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-2-1}
}
Christopher Mouron. The classification of circle-like continua that admit expansive homeomorphisms. Fundamenta Mathematicae, Tome 215 (2011) pp. 101-133. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-2-1/