We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps , with periodic critical points, we show that the inverse limit spaces and are not homeomorphic when a ≠ b. To obtain our result, we define topological substructures of a composant, called “wrapping points” and “gaps”, and identify properties of these substructures preserved under a homeomorphism.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm177-2-1,
author = {Lois Kailhofer},
title = {A classification of inverse limit spaces of tent maps with periodic critical points},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {95-120},
zbl = {1028.54038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm177-2-1}
}
Lois Kailhofer. A classification of inverse limit spaces of tent maps with periodic critical points. Fundamenta Mathematicae, Tome 177 (2003) pp. 95-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm177-2-1/