On the classification of fractal squares

Abstract

In \cite{LaLuRa13}, the authors completely classified the topological structure of so called {\it fractal square} $F$ defined by $F=(F+\mathcal{D})/n$, where $\mathcal{D}⊊\{0,1,\dots ,n-1{\}}^2,n\ge 2$. In this paper, we further provide simple criteria for the $F$ to be totally disconnected, then we discuss the Lipschitz classification of $F$ in the case $n=3$, which is an attempt to consider non-totally disconnected sets.

16 pages, 12 figures

References in corpus (2)

• Lipschitz equivalence of self-similar sets and hyperbolic boundaries
• Lipschitz Equivalence Class, Ideal Class and the Gauss Class Number Problem