报告人：田学廷（复旦大学）

邀请人：王保伟

报告题目：Searching New Phenomenon in Uniformly Hyperbolic Systems

报告时间：2020年11月10日（星期二）上午 10:00-12:00

报告地点：腾讯会议ID：996 429 974

报告摘要：One main goal in the study of Dynamical Systems is concerned with orbit structure, specifically long term or asymptotic behavior, for maps or flows. Uniformly Hyperbolic systems (such as Smale horseshoe and Anosov flow) are standard examples of complex or chaotic systems. Nowadays it is usual aiming to generalize the theory of uniform hyperbolicity to more general dynamics including nonuniform hyperbolicity and partial hyperbolicity. But in this talk we will revisit uniform hyperbolicity to introduce some new progress on searching the theory for uniformly hyperbolic systems, especially some collision phenomenon from topological perspective and probabilistic perspective including how one general orbit will go, how many types by classification and how about their dynamical complexity.

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，入选复旦大学“卓学优秀人才”计划。主要研究领域：微分动力系统与光滑遍历论。针对非一致双曲与部分双曲系统等一致双曲之外的多类动力系统，在周期逼近、跟踪性质、熵公式、SRB测度、重分形分析、Lyapunov指数等课题上取得一些进展，还对包括一致双曲系统在内的多类系统的轨道结构等方面进行了深入分析，发现了数十种统计平凡但拓扑复杂的动力学性态。已在《 Trans. AMS 》、《 Adv. Math. 》、《 Erg. The. & Dyn. Sys. 》、《 J Diff. Equat. 》等杂志上发表20余篇学术论文。所获成果已受到包括菲尔兹奖获得者Avila及一些ICM报告人在内的专家学者引用。