Ruofan Li

Dimension drop for intersections of Cantor sets

Let $E\subset \mathbb{R}$ be a self-similar set generated by a homogeneous iterated function system $\Phi$ with contraction ratio $\rho\in (0,1)$. Assume that $\Phi$ satisfies the open set condition and $\dim_{\rm H}E<1$. Let $f$ be a $C^1$-diffeomorphism on $\mathbb{R}$. We prove that if $\log|f'(x)|/\log\rho\not\in\m...