Counterexamples for IFS-attractors

Magdalena Nowak and M. Fernández-Martínez

Chaos, Solitons & Fractals, 2016, vol. 89, issue C, 316-321

Abstract: In this paper, we deal with the part of Fractal Theory related to finite families of (weak) contractions, called iterated function systems (IFS, herein). An attractor is a compact set which remains invariant for such a family. Thus, we consider spaces homeomorphic to attractors of either IFS or weak IFS, as well, which we will refer to as Banach and topological fractals, respectively. We present a collection of counterexamples in order to show that all the presented definitions are essential, though they are not equivalent in general.

Keywords: Fractal; Iterated function system; Self-similar set; Banach fractal; Topological fractal; Contraction (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:89:y:2016:i:c:p:316-321

DOI: 10.1016/j.chaos.2015.12.006

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