Diophantine property of matrices and attractors of projective iterated function systems in ${\mathbb{RP}}^1$

Boris Solomyak, Yuki Takahashi

We prove that almost every finite collection of matrices in $G{L}_d(\mathbb{R})$ and $S{L}_d(\mathbb{R})$ with positive entries is Diophantine. Next we restrict ourselves to the case $…