Dimensions of orthogonal projections of typical self-affine sets and measures

De-Jun Feng, Yu-Hao Xie

Let $T_1,\dots ,T_m$ be a family of $d\times d$ invertible real matrices with $\Vert T_i\Vert <1/2$ for $1\le i\le m$. For $\mathbf{a}=(a_1,\dots ,a_m)\in {\mathbb{R}}^{md}$, let $π^{\bf a}\…