关于举行张国华教授（复旦大学）学术报告的通知

  报告题目：Relating topological and measure-theoretic entropies of subsets

  报 告 人：张国华教授

  报告时间：2025 年 12 月 8 日 9:00-10:30

  报告地点：清清文理楼 3A01

  邀 请 人：杨启贵教授

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数学学院

2025 年 12 月 7 日

  报告人简介：

  张国华，2007 年7 月博士毕业于中国科学技术大学数学系（现为数学科学学院），2013 年起任职复旦大学数学科学学院教授。研究方向是拓扑动力系统，主要研究动力系统的复杂性理论和可数离散群作用动力系统的熵理论。在 Memoirs Amer. Math. Soc., J. Reine Angew. Math., Adv. Math., Ergod. Th. Dynam. Systems, J. Mod. Dyn., J. Funct. Anal., J.DifferentialEquations 等国际知名刊物上发表论文 40 余篇。

  报告摘要：

  Motivated by the famous Brin-Katok formula, Feng and Huang introduced the conceptsof measure-theoretical upper and lower entropies for each Borel probability measure, and establisheda variational principle relating packing and Bowen topological entropy of an analytic subset, respectively, to measure-theoretical upper and lower entropy. We show that, such a variationalprinciple fails if we consider packing and Bowen topological entropies of a general subset. Note thatBrin-Katok formula shows that, if the measure is invariant then the measure-theoretical entropies canbe defined equivalently via Kolmogorov-Sinai's idea. We show that, if the measure is not invariantthen the measure-theoretical upper and lower entropy, respectively, may differ from theKolmogorov-Sinai type entropy. These results answer negatively to some questions raised byProfessors Chen and Huang, respectively. This is a joint work with Xulei Wang.