Thresholds for one-parameter families of affine iterated function systems

This paper examines thresholds for certain properties of the attractor of a general one-parameter affine family of iterated functions systems. As the parameter increases, the iterated function system becomes less contractive, and the attractor evolves. Thresholds are studied for the following proper...

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Bibliographic Details
Published inNonlinearity Vol. 33; no. 12; pp. 6541 - 6563
Main Author Vince, Andrew
Format Journal Article
LanguageEnglish
Published 01.12.2020
Online AccessGet full text
ISSN0951-7715
1361-6544
DOI10.1088/1361-6544/aba237

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Summary:This paper examines thresholds for certain properties of the attractor of a general one-parameter affine family of iterated functions systems. As the parameter increases, the iterated function system becomes less contractive, and the attractor evolves. Thresholds are studied for the following properties: the existence of an attractor, the connectivity of the attractor, and the existence of non-empty interior of the attractor. Also discussed are transition phenomena between existence and non-existence of an attractor.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aba237