Separation properties for self-conformal sets
Volume 152 / 2002
Studia Mathematica 152 (2002), 33-44
MSC: Primary 28A78, 54E40; Secondary 54H15.
DOI: 10.4064/sm152-1-3
Abstract
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.
