学术报告报告题目：Dynamical behavior that are statistically trivial but topologically complicated in chaotic systems
报 告 人：田学廷教授（复旦大学）
报告时间：2021年5月11日（星期二）下午14:00---15:00
报告地点：腾讯会议：会议 ID：352 157 165，会议密码：654321
邀 请 人：马东魁教授
欢迎广大师生前往！
数学学院
2021年05 月08 日
报告摘要：
In a dynamical system, by known Poincare recurrence theorem, Birkhoff ergodic theorem and Oseledec multiplicative ergodic theorem, there exists a totally full measure set such that every point in this set is recurrent and its orbit enters in its neighborhood with positive lower density, the set of its emprical measures of time average is a singleton corresponding to an ergodic measure, and the Lyapunov exponents at this point with respect to the derivative of a differential system or a cocycle exist. However, it has been found that the points without exitence of time average can carry full topological entropy and strong distributional chaos in various chaotic systems including symbolic systems, uniformly hyperbolic systems and some known non-uniformly hyperbolic systems such as Katok map, Mane examples etc. In this talk we will consider more different asymptotic behavior and show that they are usually statistically trivial but topologically complicated in various chaotic systems: (1) Lyapunov irregular points can carry full topological entropy and strong distributional chaos; (2) Points without SRB or SRB-like behavior can carry full topological entropy and strong distributional chaos; (3) Points with or without transitive behavior, recurrent behavior by using different frequency can form more than thirty different dynamical behavior, most of which are discovered to be statistically trivial but all carry strong topological complexity in the sense of full topological entropy and distributional chaos.
报告人简介：
田学廷，现为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。已在Trans. AMS 、Adv. Math. 、Erg. The. & Dyn. Sys. 、Ann. I H Poincare- PR、Math. Z.、J Diff. Equat. 、Nonlinearity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。