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arXiv · 1912.03220

Thresholds for One-Parameter Families of Affine Iterated Function Systems

Andrew Vince
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Abstract

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.

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Andrew Vince. 2019-12-06. Thresholds for One-Parameter Families of Affine Iterated Function Systems. https://doi.org/10.1088/1361-6544/aba237

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