Lipschitz equivalence of graph-directed fractals
Volume 194 / 2009
Studia Mathematica 194 (2009), 197-205
MSC: Primary 28A80.
DOI: 10.4064/sm194-2-6
Abstract
This paper studies the geometric structure of graph-directed sets from the point of view of Lipschitz equivalence. It is proved that if $\{E_{i}\}_{i}$ and $\{F_{j}\}_{j}$ are dust-like graph-directed sets satisfying the transitivity condition, then $E_{i_{1}}$ and $E_{i_{2}}$ are Lipschitz equivalent, and $E_{i}$ and $F_{j}$ are quasi-Lipschitz equivalent when they have the same Hausdorff dimension.
