报告人：何育彬 副教授（汕头大学）

时间：2026年3月29日 15:00-

地点：理科楼LA104

摘要：Let K be a self-similar set in R^d satisfying the open set condition. We obtain a sharp upper bound as well as several nontrivial lower bounds for the Hausdorff dimension of the set of inhomogeneous τ-well approximable points in K when τ is below a certain threshold.

One of these lower bounds is shown to be sharp in the one-dimensional case when K is sufficiently “thick”, and in this situation the corresponding set also has full Hausdorff measure. These results have several applications:

(1) the set of homogeneous very well approximable numbers has full Hausdorff dimension within strongly irreducible self-similar sets in R^d;

(2) the set of inhomogeneous very well approximable numbers has full Hausdorff dimension within sufficiently thick missing-digit sets in R.

We also construct certain nontrivial missing-digit sets K in R^d with d ≥ 2 for which the intersection of K with the set of τ-well approximable points has full Hausdorff measure.

邀请人：孔德荣