On a family of IFSs whose attractors are not connected
type: Item
instance of: scholarly article
title: On a family of IFSs whose attractors are not connected
zbMATH Open document ID: 1208.28007
author: Alexandru Mihail
author: Radu Miculescu
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-02-09T00:00:00Z
review text: On a given Banach space \(X\), the authors consider a family of Iterated Function Systems (IFSs) composed by two affine contractions and indexed by the free term of the second contraction, such that the linear operator from the definition of the first contraction is finite dimensional. Using a well known result concerning the connectivity of the attractor of an IFS, they prove that the set of the free terms of the second contraction for which the attractor is disconnected is open and dense in \(X\). In this way, a connection between the theory of IFSs and the theory of finite dimensional operators is established.
reviewed by: Nicolae-Adrian Secelean
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 5848870
zbMATH Keywords: iterated function systems
zbMATH Keywords: attractors
zbMATH Keywords: connectivity
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.10.039
OpenAlex ID: W2019423485
cites work: Q4040874
cites work: Q4351902
cites work: Q3652485
cites work: Q3995301
cites work: Q3731958
cites work: Analysis on fractals
cites work: On the connectivity of attractors of iterated multifunction systems
DOI: 10.1016/J.JMAA.2010.10.039
description: scientific article; zbMATH DE number 5848870