Speaker: Han Yu
25 November, 2020 14:30 UTC
Abstract: We show that the rational points are quite well ‘equidistributed’ near the middle 15th Cantor set $K$. As a consequence, it is possible to show that the set of well-approximable numbers has full Hausdorff dimension inside $K$. This answers a question of Levesley-Salp-Velani for $K$. In fact, it is possible to prove a slightly stronger result which partially answers a question of Bugeaud-Durand. The results also hold for some self-similar sets other than $K$. We will provide a sufficient condition and some other examples. We suspect that the above results hold for all self-similar sets with Hausdorff dimension bigger than $12\frac{1}{2}$ and with the open set condition. We will see some heuristics in the talk.