Rigidity theorem of graph-directed fractals

DOI10.4310/AJM.2018.V22.N6.A8zbMATH Open1407.28003arXiv1308.3143WikidataQ128442126 ScholiaQ128442126MaRDI QIDQ1717138

Ying Xiong, Li-Feng Xi

Publication date: 7 February 2019

Published in: The Asian Journal of Mathematics (Search for Journal in Brave)

Abstract: In this paper, we identify two fractals if and only if they are biLipschitz equivalent. Fix ratio $r,$ for dust-like graph-directed sets with ratio $r$ 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.

Full work available at URL: https://arxiv.org/abs/1308.3143

zbMATH Keywords

fractalself-similar setgraph-directed setsbilipschitz equivalence

Mathematics Subject Classification ID

Fractals (28A80)

Related Items (2)

Fractal property of the graph homomorphism order ⋮ On multifractal rigidity

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