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/