Attractors of iterated function systems with uncountably many maps and infinite sums of Cantor sets
type: Item
instance of: scholarly article
title: Attractors of iterated function systems with uncountably many maps and infinite sums of Cantor sets
zbMATH Open document ID: 1396.28016
DOI: 10.4171/JFG/50
author: Giorgio Mantica
author: Roberto Peirone
published in: Journal of Fractal Geometry
publication date: 2017-11-17T00:00:00Z
review text: The authors consider iterated function systems on the real line, consisting of affine maps of homogeneous contraction ratio, and study the topological properties of their attractors. There are uncountably many such objects and the set of their fixed points is a Cantor set. They prove that, under specific hypotheses, such attractors consist of the union of a finite number of closed intervals, and a more general result for infinite sums of compact sets, in the sense of Minkowski and under the Hausdorff metric.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 37C20
Mathematics Subject Classification ID: 37E05
zbMATH DE Number: 6808298
zbMATH Keywords: Cantor sets
zbMATH Keywords: iterated function systems
zbMATH Keywords: second generation IFS
zbMATH Keywords: attractors
zbMATH Keywords: Minkowski sums
zbMATH Keywords: series of Cantor sets
reviewed by: George Stoica
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6808298