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报告人 ：黄良益（北京理工大学）

日期：2020年10月14日

时间：上午 10:30

地址：数统91直播 LD202

报告摘要：We study multifractal properties of Bernoulli measure $\mu_p$ for homogeneous Cantor set determined by $([0,1], (2)_{k\ge 1}, (c_k)_{k\ge 1})$, where $0<p<1/2$ and $c_k$ is either $d_1$ or $d_2$ with $0<d_1<d_2<1/2$. It is proved by Wu (Sci. China, 2005) that if the occurrence frequency of $d_1$ in $(c_k)_{k\ge 1}$ exists, then the multifractal formalism holds. We show that if the frequency does not exist, then the multifractal formalism and Olsen’s refined multifractal formalism hold in some condition, and do not hold in other conditions. This answers one of the questions asked by Olsen (Adv. Math. 1995.)

报告人简介：黄良益，北京理工大学博士，导师是刘庆晖教授，主要研究方向为分形几何。

联系人：罗军

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