Approximation on the Cantor set and some of its inhomogeneous friends
Ergodic Theory and Dynamical Systems Seminar
31st January 2019, 2:00 pm – 3:00 pm
Howard House, 4th Floor Seminar Room
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).