Counterexamples for IFS-attractors

Área de investigación: Applied Mathematics Año: 2016
Tipo de publicación: Artículo Palabras clave: Fractal; Iterated function system; Self-similar set; Banach fractal; Topological fractal; Contraction
Autores: Nowak, Magdalena; Fernández Martínez, Manuel
Journal: Chaos, Solitons & Fractals Volumen: 89
Páginas: 316-321
Mes: August
ISSN: 0960-0779
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.
Texto completo: paper.pdf