The Conley Attractor of an Iterated Function System

2012/06/27 by Michael F. Barnsley, Barnsley, Michael, Andrew Vince +1 · 2 citations
Mathematics · #28A80 #37C70 #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1206.6319

openalex publication_date 2012/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Iterated function systems with the average shadowing property
• Parameterized IFS with the asymptotic average shadowing property

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