Separation properties for self-conformal sets

Volume 152 / 2002

Yuan-Ling Ye Studia Mathematica 152 (2002), 33-44 MSC: Primary 28A78, 54E40; Secondary 54H15. DOI: 10.4064/sm152-1-3


For a one-to-one self-conformal contractive system $\{ w_{j} \}_{j=1}^{m}$ on ${\mathbb R}^{d}$ with attractor $K$ and conformality dimension $\alpha$, Peres et al. showed that the open set condition and strong open set condition are both equivalent to $0 < {\cal H}^{\alpha}(K)<\infty$. We give a simple proof of this result as well as discuss some further properties related to the separation condition.


  • Yuan-Ling YeDepartment of Mathematics
    The Chinese University of Hong Kong
    Shatin, Hong Kong
    Department of Mathematics
    South China Normal University
    Guangzhou 510631, P.R. China

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