Lipschitz equivalence of a class of self-similar sets

TL;DR

This paper investigates conditions under which certain self-similar fractal sets with overlaps are Lipschitz equivalent, providing a mathematical criterion for their geometric similarity.

Contribution

It offers a new sufficient condition for Lipschitz equivalence among a class of self-similar sets with overlaps, advancing understanding of their geometric classification.

Findings

Established a sufficient condition for Lipschitz equivalence

Applied the condition to a class of self-similar sets with overlaps

Enhanced the classification framework for fractal sets

Abstract

We consider a class of homogeneous self-similar sets with complete overlaps and give a sufficient condition for the Lipschitz equivalence between members in this class.