On the classification of inverse limits of tent maps
Volume 187 / 2005
Fundamenta Mathematicae 187 (2005), 171-192
MSC: Primary 54F15; Secondary 37E05, 37B45.
DOI: 10.4064/fm187-2-5
Abstract
Let $f_s$ and $f_t$ be tent maps on the unit interval. In this paper we give a new proof of the fact that if the critical points of $f_s$ and $f_t$ are periodic and the inverse limit spaces $(I,f_s)$ and $(I,f_t)$ are homeomorphic, then $s = t$. This theorem was first proved by Kailhofer. The new proof in this paper simplifies the proof of Kailhofer. Using the techniques of the paper we are also able to identify certain isotopies between homeomorphisms on the inverse limit space.
