Homeomorphisms generated from overlapping affine iterated function systems
Michael F. Barnsley, Brendan Harding, Andrew Vince
TL;DR
This paper develops a theoretical framework for creating fractal homeomorphisms using pairs of overlapping affine iterated function systems, expanding understanding of their mathematical properties.
Contribution
It introduces a novel approach to generate fractal homeomorphisms from overlapping affine IFS pairs, filling a gap in the mathematical theory.
Findings
Established conditions for fractal homeomorphisms from overlapping affine IFS
Provided new methods for constructing such homeomorphisms
Enhanced understanding of the structure of fractal transformations
Abstract
We develop the theory of fractal homeomorphisms generated from pairs of overlapping affine iterated function systems.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Chaos control and synchronization