Comparison of the sets of attractors for systems of contractions and weak contractions

Paweł Klinga and Adam Kwela

Chaos, Solitons & Fractals, 2022, vol. 155, issue C

Abstract: For n,d∈N we consider the families:•Lnd of attractors for iterated function systems (IFS) consisting of n contractions acting on [0,1]d,•wLnd of attractors for weak iterated function systems (wIFS) consisting of n weak contractions acting on [0,1]d.We study closures of the above families as subsets of the hyperspace K([0,1]d) of all compact subsets of [0,1]d equipped with the Hausdorff–Pompeiu metric. In particular, we show that Lnd¯=wLnd¯ and Ln+1d∖Lnd¯≠∅, for all n,d∈N. What is more, we construct a compact set belonging to L2d¯ which is not an attractor for any wIFS. We present a diagram summarizing our considerations.

Keywords: Attractors; Iterated function systems; Weak iterated function systems (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921011188

DOI: 10.1016/j.chaos.2021.111764

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