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Spring Topology and Dynamics Conference 2006
March 23-25, 2006
University of North Carolina at Greensboro
Greensboro, NC, USA

Organizers
Gregory Bell, Alexander Chigogidze, Paul Duvall, Jan Rychtar, Jerry Vaughan

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On Ingram's Conjecture
by
James Keesling
University of Florida
Coauthors: Slagjana Jakimovik (Cyril and Methodius University) Louis Block (University of Florida)

Let f:[0, 1] → [0, 1] be a tent map with slope s between 1 and 2. Let Xs be the inverse limit space obtained from an inverse sequence with f being the only bonding map. The Ingram Conjecture is the conjecture that if Xs and Xt are homeomorphic, then s=t. There are solutions for the conjecture if f has certain restrictions such as having periodic turning point. The authors propose an approach which would prove the conjecture without restriction. One link in this program remains unsolved. A conjecture is proposed which, if true, would solve the remaining link and thus provide a proof of Ingram's Conjecture.

Date received: February 27, 2006

Copyright © 2006 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cast-08.