报告人 ：饶辉（华中师范大学）

日期：2020年7月3日

时间：上午10：00 - 12:00

腾讯会议 ID：841 128 291

会议连接：https://meeting.tencent.com/s/09otsPnWn7EE

报告摘要：We study the bi-Lipschitz classification of Bedford-McMullen carpets which are totally disconnected. Let $E$ be a such carpet and let $\mu_E$ be the uniform Bernoulli measure on $E$. We show that the multifractal spectrum of $\mu_E$ is a bi-Lipschitz invariant, and the doubling property of $\mu_E$ is also invariant under a bi-Lipschtz map. We show that if $E$ and $F$ are totally disconnected and that $\mu_E$ and $\mu_F$ are doubling, then a bi-Lipschitz map between $E$ and $F$ enjoys a measure preserving property. Thanks to the above results, we give a complete classification of Bedford-McMullen carpets which are regular (that is, its Hausdorff dimension and box dimension coincides,) or satisfy a separation condition due to [J. F. King, The Singularity spectrum for general sierpinski carpets, \textit{Adv. Math.} \textbf{116} (1995), 1-11].

报告人简介：饶辉，1995年博士毕业于武汉大学，现为华中师范大学教授、博导，研究方向为分形几何、符号动力系统与Tiling理论。饶老师在Pisot谱猜测、自仿tile的数字集结构、以及自相似集的Lipschitz 等价等国际热门问题上做出了一系列开创性研究成果，在国内外颇具影响力。目前已在Adv. Math., JMPA, TAMS等著名数学杂志发表论文56篇，主持国家自然科学基金面上项目多项。

联系人：罗军

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