重庆大学罗军教授学术报告6月2日上午
发布时间: 2018-05-31 访问次数: 15

学术讲座【On the Lipschitz equivalence of self-affine sets

  

时间:201862(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.