Morse decompositions of uniform random attractors

主讲人：曾才斌 华南理工大学副教授

时间：2022年11月11日9：00

地点：腾讯会议 560 281 250

举办单位：数理学院

主讲人介绍：曾才斌，副教授，博士生导师。现任职于华南理工大学数学学院，主要从事随机微分方程与动力系统的研究。主持国基面上2项、国基青年、国基天元与3项省部级项目，在JDE、Chaos等期刊发表三十余篇学术论文。

内容介绍：In this talk we report the Morse theory on uniform random attractors for non-autonomous random dynamical systems. To handle the non-invariance of uniform random attractors, we construct the Morse sets of uniform random attractor as the projections of the Morse sets on pullback attractor of the skew product semiflow. First, we obtain the Morse decomposition of uniform random attractors in probability. Second, we describe a decaying energy level on such attractor by Lyapunov function with probability one. Furthermore, we study the stability of Morse decompositions of deterministic uniform attractor under a small random disturbance. Finally, we discuss and collect the results on the Morse decomposition under random setting.