Lipschitz equivalence of graph-directed fractals

Volume 194 / 2009

Ying Xiong, Lifeng Xi Studia Mathematica 194 (2009), 197-205 MSC: Primary 28A80. DOI: 10.4064/sm194-2-6


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.


  • Ying XiongDepartment of Mathematics
    South China University of Technology
    Guangzhou, 510641, P.R. China
  • Lifeng XiInstitute of Mathematics
    Zhejiang Wanli University
    Ningbo, Zhejiang, 315100, P.R. China

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