报告人：廖灵敏（法国东巴黎大学）

时间：2021年11月16日9:30开始

腾讯会议ID：626 746 131（无密码）

摘要：Multifractal analysis of Birkhoff averages of a (real-valued) function in a given dynamical system aims at determining the Hausdorff dimension of the set of points with given limit of the Birkhoff averages. Such study dates back to the classical results of Besicovitch (1934) and Eggleston (1949) on the Hausdorff dimension of the set of numbers with prescribed frequency of the digit 1 in their dyadic expansions. The corresponding question for continued fraction expansion, which involves some symbolic dynamics on an alphabet of infinite symbols, has attracted much attention. We will see that the key to the solution is a delicate construction of Cantor subset with Hausdorff dimension one-half. To do multifractal analysis of the Birkhoff averages of other functions, we also use the Ruelle transfer operator theory. We will see how such theory provides us suitable measures supported on the sets in question which help us finding the Hausdorff dimension.

简介:廖灵敏，法国东巴黎大学副教授，博士生导师。主要从事分形几何，动力系统，度量数论等方面的研究。主持或参与法国国家科研计划，法国台湾幽兰合作计划，法国中国蔡元培合作计划，法国韩国星合作计划，法国波兰钋合作计划等。曾应邀在瑞典，波兰，韩国，巴西，马来西亚等国家访问讲学。 在包括J.Eur.Math.Soc., Math.Ann., Adv. Math., Int.Math.Res.Not., Trans.Amer.Math.Soc., Ergod.Theory Dyna.Syst.等在内的国际期刊发表论文37篇。

邀请人：孔德荣

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