From the discrete to the continuous
by
Judy Kennedy
Dept of Math Sciences, University of Delaware

Horseshoe maps have played a key role in dynamical systems. Here we examine the topological aspects in which no hyperbolicity or even derivatives are assumed. Suppose X denotes a compact metric space, A denotes a closed subset of X, and f is homeomorphism from X to itself under which A is invariant. We consider two situations and their consequences: (1) Suppose f on A factors over an m-shift (with m>1) on a Cantor set. (2) Suppose an m-shift (m>1) on a Cantor set factors over f on A. By "horseshoe map" we mean that shift dynamics are involved as in situation 1. Situation 2 leads to a sort of "collapsed horseshoe" in many cases.

Date received: February 8, 1999

Copyright © 1999 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 # caca-28.