Ratio geometry, rigidity and the scenery process for hyperbolic Cantor sets

Tim Bedford, Albert M. Fisher

Given a $C^{1+\gamma }$ hyperbolic Cantor set $C$, we study the sequence $C_{n,x}$ of Cantor subsets which nest down toward a point $x$ in $C$. We show that $C_{n,x}$ is asymptotically e…