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Attractors and Inverse Limits.

James Keesling — 2008

RACSAM

This paper surveys some recent results concerning inverse limits of tent maps. The survey concentrates on Ingram’s Conjecture. Some motivation is given for the study of such inverse limits.

On the classification of inverse limits of tent maps

Louis BlockSlagjana JakimovikLois KailhoferJames Keesling — 2005

Fundamenta Mathematicae

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.

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