Dimension of affine iterated function systems on ${\mathbb{R}}^d$

Jialun Li, Wenyu Pan, Zhiyuan Zhang

Let $\{f_i(x)=M_{i}x+a_i{\}}_{i\in I}$ be an affine iterated function system on ${\mathbb{R}}^d$ with attractor $\Lambda$, and let $\mu$ be an associated self-affine measure. Assume that the $M_…