Demi Allen

Approximation on the Cantor set and some of its inhomogeneous friends

In 2007, Levesley, Salp, and Velani showed that the Hausdorff measure of the set of points in the middle-third Cantor set which can be approximated by triadic rationals at a given rate of approximation satisfies a zero-full dichotomy. More precisely, the Hausdorff measure of the set in question is either zero or full according to, respectively, the convergence or divergence of a certain sum which is dependent on the specified rate of approximation. In this talk, I will discuss an analogue of this result in the setting of more general self-similar sets with inhomogeneous contraction ratios. This talk is based on ongoing joint work with Balázs Bárány (Budapest).