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Searching New Phenomenon in Uniformly Hyperbolic Systems: Conditional Intermediate Entropy Property
日期: 2022-11-18      信息来源:      点击数:

走向现代数学学术报告 - 田学廷教授(No. 559)

报告题目:Searching New Phenomenon in Uniformly Hyperbolic Systems: Conditional Intermediate Entropy Property

报 告 人:田学廷 教授(复旦大学)

报告时间:2022年11月24日 上午9:00

腾讯会议ID:190-717-302

摘要:In recent years we try to find some new phenomenon in chaotic dynamics and have obtained many observations on recurrence, non-recurrence, SRB behavior, Lyapunov irregularity, intermediate entropy property, emergence etc from various viewpoints. In this talk we mainly consider the problem of intermediate entropy property under certain conditions and have obtained some refined results. For example, we find that every level set of the Birkhoff average over an observable function has the intermediate entropy property. This result applies to many kinds of systems, including uniformly hyperbolic systems and some systems beyond (e.g. general homoclinic classes and singular-hyperbolic flows), symbolic systems, etc. The idea of its proof is mainly based on the construction of a property called multi-horseshoe property and the coordination of many classical ergodic theories.

报告人简介:田学廷,现任复旦大学数学科学学院教授,博士生导师。主要研究动力系统的拓扑理论和遍历理论,已在Adv.Math.Trans.AMSErg.Th.Dyn.Syst.等杂志上发表20余篇学术论文,受到包括一些Fields奖获得者和ICM报告人在内的专家学者的引用。

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