Dynamical System Topology Preserved in the Presence of Noise
by
Judy Kennedy
University of Delaware
Coauthors: James A. Yorke (University of Maryland)

We first give precise definitions of the terms "generalized quadrilateral" and "topological horseshoe", and then examine the behavior of a homeomorphism F on locally compact, separable, locally connected metric space X such that F restricted to some generalized quadrilateral Q in X is a topological horseshoe map. We prove that there are various invariant indecomposable sets and Cantor sets associated with such maps, and that n-shift dynamics are involved. Next we prove that even when small amounts of noise are added to the dynamical system, there are associated indecomposble sets and Cantor sets, although it is no longer possible to talk about invariant sets.

Date received: February 26, 1997

Copyright © 1997 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 # caam-23.