Size of the set of attractors for iterated function systems

Paweł Klinga, Adam Kwela and Marcin Staniszewski

Chaos, Solitons & Fractals, 2019, vol. 128, issue C, 104-107

Abstract: We discuss the smallness of the set of attractors for iterated function systems. This paper is an attempt to measure the difference between the family of IFS attractors and a broader family, the set of attractors for the weak iterated function systems. We prove that the IFS attractors form a σ-porous subset of K([0, 1]d), the family of compact subsets of a metric space [0, 1]d. We also show that weak IFS attractors form a first category set.

Keywords: Attractors; Iterated function systems; Porosity; σ-porosity (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:128:y:2019:i:c:p:104-107

DOI: 10.1016/j.chaos.2019.07.028

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