A classification of inverse limit spaces of tent maps with periodic critical points
Volume 177 / 2003
Fundamenta Mathematicae 177 (2003), 95-120
MSC: Primary 54F15; Secondary 54H20, 58F03.
DOI: 10.4064/fm177-2-1
Abstract
We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps $f_a$, $f_b$ with periodic critical points, we show that the inverse limit spaces $({\mathbb I}_a,f_a)$ and $({\mathbb I}_b,g_b)$ are not homeomorphic when $a \neq b$. 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.
