Relational generalized iterated function systems

Izabella Abraham, Radu Miculescu and Alexandru Mihail

Chaos, Solitons & Fractals, 2024, vol. 182, issue C

Abstract: In this paper, we introduce a wider class of generalized iterated function systems, called relational generalized iterated function systems. More precisely, the classical contraction condition for functions defined on product spaces is weakened by means of an equivalence relation. In particular, if we consider the total equivalence relation, we recover the classical generalized iterated function systems. Our main result states that each compact subset of the underlying metric space generates, via a sequence of iterates, a fixed point of the associated fractal operator, called an attractor of the system. We also establish a structure result for the attractors and a theorem concerning the continuous dependence of the attractor on the associated compact set. Ultimately, we provide some examples which illustrate our main results.

Keywords: Equivalence relations; Relational generalized iterated function systems; Attractors; Weakly Picard operators (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003758

DOI: 10.1016/j.chaos.2024.114823

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