走向现代数学学术报告 - 刘学博士（No.596）

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

报 告 人：刘学 博士（中国科学技术大学）

报告时间：2023年4月16日（星期日） 14:30

报告地点：工西416（学术报告厅）

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.

报告人简介：刘学，2021年博士毕业于美国Brigham Young University，现在中国科学技术大学数学学科学院从事博士后研究工作，研究方向为动力系统与遍历理论，在 Proc. Amer. Math. Soc.等期刊发表学术论文。