Atlas home || Conferences | Abstracts | about Atlas

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

View Abstracts
Conference Homepage

Characterizing Tent-like maps
by
Stewart Baldwin
Auburn University

The following definition is an obvious generalization of "tent" maps on an interval.



Definition: A map f:X → X of a continuum X is called tent-like if there is a constant l > 1, a metric d on X generating the topology, and two subcontinua C1 and C2 with C1 ∪C2=X such that for any i=1, 2 and any two points x, y of Ci, d(f(x), f(y))=ld(x, y).


In the case where X is a dendrite and the metric d is required to be a taxicab metric, there is an elegant characterization of the property in terms of kneading sequences. In this case, the constant l is unique and the metric d is unique up to scale. We discuss recent attempts to generalize these results to spaces X which are not dendrites.

Date received: February 28, 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-22.