A separation property for iterated function systems of similitudes

De-Jun Feng, Huo-Jun Ruan, Ying Xiong

Let $E$ be the attractor of an iterated function system $\{{\varphi }_i(x)=\rho R_{i}x+a_i{\}}_{i=1}^N$ on ${\mathbb{R}}^d$, where $0<\rho <1$, $a_i\in {\mathbb{R}}^d$ and $R_i$ are orthogonal transformations on $…