Dimension of Furstenberg measures on ${\mathbb{CP}}^1$

Ariel Rapaport, Haojie Ren

Let $\hat{I}¸$ be a finitely supported probability measure on $\mathrm{SL}(2,\mathbb{C})$, and suppose that the semigroup generated by $\mathcal{G}:=\mathrm{supp}(\hat{I}¸)$ is strongly irredu…