Dimension of diagonal self-affine sets and measures via non-conformal partitions

Ariel Rapaport

Let $\Phi :={\left\{(x_1,...,x_d)\to \left(r_{i,1}{x}_1+a_{i,1},...,r_{i,d}{x}_d+a_{i,d}\right)\right\}}_{i\in \Lambda }$ be an affine diagonal IFS on ${\mathbb{R}}^d$. Suppose that…