Thresholds for One-Parameter Families of Affine Iterated Function Systems
Metric Geometry
2020-12-02 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1912.03220,
title = {Thresholds for One-Parameter Families of Affine Iterated Function Systems},
author = {Andrew Vince},
journal= {arXiv preprint arXiv:1912.03220},
year = {2020}
}