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THE CONLEY ATTRACTORS OF AN ITERATED FUNCTION SYSTEM

Part of: Classical measure theory Smooth dynamical systems: general theory

Published online by Cambridge University Press:  11 June 2013

MICHAEL F. BARNSLEY  and
ANDREW VINCE
MICHAEL F. BARNSLEY
Affiliation:
Department of Mathematics, Australian National University, Canberra, ACT, Australia email [email protected]@aol.com
ANDREW VINCE*
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA
*
✉[email protected]
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Abstract

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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 of Kieninger [Iterated Function Systems on Compact Hausdorff Spaces (Shaker, Aachen, 2002)] and McGehee and Wiandt [‘Conley decomposition for closed relations’, Differ. Equ. Appl. 12 (2006), 1–47] restricted to what is, in many ways, a simpler setting, but focused on a special type of attractor, namely point-fibred invariant sets. This allows us to give short proofs of some of the key ideas.

Keywords

iterated function systemattractor–repeller

MSC classification

Secondary: 37C70: Attractors and repellers, topological structure 28A80: Fractals
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 2 , October 2013 , pp. 267 - 279
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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