On normal numbers and self-similar measures

Amir Algom, Simon Baker, Pablo Shmerkin

Let $\{f_i(x)=s_i\cdot x+t_i\}$ be a self-similar IFS on $\mathbb{R}$ and let $\beta >1$ be a Pisot number. We prove that if $\frac{\log |s_i|}{\log \beta }\notin \mathbb{Q}$ fo…