arXiv Analytics

Sign in

arXiv:1206.6319 [math.DS]AbstractReferencesReviewsResources

The Conley Attractor of an Iterated Function System

Michael Barnsley, Andrew Vince

Published 2012-06-27Version 1

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.

Comments: 12 pages, 2 figures
Categories: math.DS, math.GN
Subjects: 37C70, 28A80
Related articles: Most relevant | Search more
arXiv:2009.01482 [math.DS] (Published 2020-09-03)
Takens-type reconstruction theorems of one-sided dynamical systems on compact metric spaces
arXiv:0910.1958 [math.DS] (Published 2009-10-10, updated 2011-11-07)
On μ-Compatible Metrics and Measurable Sensitivity
arXiv:math/0608257 [math.DS] (Published 2006-08-10)
Every compact metric space that supports a positively expansive homeomorphism is finite

Links

Toolbox