2013/08/14 by Lifeng Xi, Li-Feng Xi, Ying Xiong +2
Mathematics · #28A80 #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #math.MG #msc:28A80
paper · pdf · doi:10.48550/arxiv.1308.3143
27 pages, 7 figures
arxiv created 2013/08/14 · openalex publication_date 2013/08/14 · arxiv updated 2013/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.