Rigidity Theorem of Graph-directed Fractals
Metric Geometry
2013-08-15 v1
Abstract
In this paper, we identify two fractals if and only if they are biLipschitz equivalent. Fix ratio for dust-like graph-directed sets with ratio and integer characteristics, we show that they are rigid in the sense that they are uniquely determined by their Hausdorff dimensions. Using this rigidity theorem, we show that in some class of self-similar sets, two totally disconnected self-similar sets without complete overlaps are biLipschitz equivalent.
Keywords
Cite
@article{arxiv.1308.3143,
title = {Rigidity Theorem of Graph-directed Fractals},
author = {Li-Feng Xi and Ying Xiong},
journal= {arXiv preprint arXiv:1308.3143},
year = {2013}
}
Comments
27 pages, 7 figures