The Conley Attractor of an Iterated Function System
Dynamical Systems
2012-06-28 v1 General Topology
Abstract
We investigate the topological and metric properties of attractors of an iterated function system (IFS) whose functions may not be contractive. We focus, in particular, on invertible IFSs of finitely many maps on a compact metric space. We rely on ideas Kieninger and McGehee and Wiandt, restricted to what is, in many ways, a simpler setting, but focused on a special type of attractor, namely point-fibred minimal (locally) invariant sets. This allows us to give short proofs of some of the key ideas.
Cite
@article{arxiv.1206.6319,
title = {The Conley Attractor of an Iterated Function System},
author = {Michael Barnsley and Andrew Vince},
journal= {arXiv preprint arXiv:1206.6319},
year = {2012}
}
Comments
12 pages, 2 figures