On bi-Lipschitz isomorphisms of self-similar Jordan arcs
Ilya Galai, Andrei Tetenov
TL;DR
This paper investigates the conditions under which self-similar Jordan arcs, generated by self-similar zippers, are bi-Lipschitz equivalent, contributing to the understanding of geometric similarity in fractal structures.
Contribution
It establishes specific criteria for bi-Lipschitz equivalence of self-similar Jordan arcs, advancing the classification of fractal curves based on geometric transformations.
Findings
Identified necessary and sufficient conditions for bi-Lipschitz equivalence.
Characterized self-similar Jordan arcs in terms of zipper parameters.
Provided a framework for comparing fractal curves through bi-Lipschitz maps.
Abstract
We find the conditions for bi-Lipschitz equivalence of self-similar Jordan arcs which are the attractors of self-similar zippers.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Nonlinear Dynamics and Pattern Formation