学术讲座【On the Lipschitz equivalence of self-affine sets】
时间：2018年6月2日(星期六)上午10:15-11:15
地点：理工北楼601报告厅
主办：数学与信息学院, 福建省分析数学及应用重点实验室, 数学研究中心
主讲：重庆大学，罗军教授
参加对象：数学系老师及研究生
专家简介：重庆大学数学系教授，博士。主要从事分形集的lipschitz等价性，分形集的连通性，自仿测度的谱性质等研究。
报告摘要：Let $A$ be an expanding $d\2018-06-02 (星期六) 10:15-11:15 d$ matrix with integer entries and $\D\subset \Z$ be a finite digit set. Then the pair $(A, \D)$ defines a unique integral self-affine set $K=A^{-1}(K+\D)$. In this paper, by replacing the Euclidean norm with a pseudo-norm $w$ in terms of $A$, we construct a hyperbolic graph on $(A, \D)$ and show that $K$ can be identified with the hyperbolic boundary. Moreover, if $(A, \D)$ safisfies the open set condition, we also prove that two totally disconnected integral self-affine sets are Lipschitz equivalent if an only if they have the same $w$-Hausdorff dimension, that is, their digit sets have equal cardinality.We extend some well-known results in the self-similar sets to the self-affine sets.