題 目：討論M_0集的定量逼近性質(zhì)
時(shí) 間：2025年9月11日（星期四）19:00
主講人：周青龍
地 點(diǎn)：騰訊會(huì)議（會(huì)議號(hào)809448684）
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
主講人簡(jiǎn)介：周青龍，武漢理工大學(xué)理學(xué)院數(shù)學(xué)系副教授，碩士生導(dǎo)師。主要從事分形幾何與動(dòng)力系統(tǒng)、丟番圖逼近與度量數(shù)論的研究工作。
講座簡(jiǎn)介：
Let E ? [0, 1)^d be a set supporting a probability measure μ with
Fourier decay |u ?(t)| ? (log |t|)^{?s} for some constant s > d + 1. Consider a
sequence of expanding integral matrices A=〖(A_n)〗_(n∈N) such that the minimal
singular values of A_(n+1) 〖A_n〗^(-1)are uniformly bounded below by K > 1. We
prove a quantitative Schmidt-type counting theorem under the following constraints:
(1) the points of interest are restricted to E; (2) the denominators of
the “shifted” rational approximations are drawn exclusively from A. Our result
extends the work of Pollington, Velani, Zafeiropoulos, and Zorin (2022) to
the matrix setting, advancing the study of Diophantine approximation on fractals.
Moreover, it strengthens the equidistribution property of the sequence
〖(A_n X)〗_(n∈N) for μ-almost every x ∈ E. Applications include the normality of
vectors and shrinking target problems on fractal sets.
