报告题目：Multifractal analysis for a class of skew product transformations

报告人：刘学副研究员（东南大学）

报告时间：2024年6月15日上午9:00-10:00

报告地点：数学院一楼135报告厅

报告摘要：In this talk, we give a multifractal analysis on the Birkhoff average for a class of skew product transformations, which is driven by a uniquely ergodic homeomorphism and satisfies Anosov and topological mixing on fibers property. The conclusion is twofold: a variational principle between the fiber Bowen’s topological entropy on conditional level sets of Birkhoff average and fiber measure-theoretical entropy; If the irregular set is nonempty on some fibers, then on almost every fiber with respect to the unique ergodic measure, it is nonempty and carries full fiber Bowen’s topological entropy. Examples of systems under consideration are provided.

个人简历：刘学，东南大学副研究员，博士毕业于美国BrighamYoung University,博士导师为吕克宁教授，博士毕业后，在中国科学技术大学黄文教授指导下从事博士后研究工作。研究领域为动力系统遍历理论。相关工作发表在J. of Differential Equations, Discrete and Contin. Dyn. Syst., Proc. Amer. Math. Soc.，Phys. Scr.以及 J. Math. Anal. Appl.等国际专业杂志。