Morse decomposition for random dynamical systems

发布者:文明办发布时间:2019-06-27浏览次数:535


主讲人:柳振鑫 大连理工大学教授 博士生导师


时间:2019年7月3日13:00


地点:3号楼301室


举办单位:数理学院


主讲人介绍:柳振鑫,大连理工大学数学科学学院教授、博士生导师。主要从事随机动力系统的研究;在随机Conley指标理论、随机回复运动、平稳分布等方面做出系统深入的研究工作。


内容介绍:The Morse decomposition theorem states that a compact invariant set of a given ?flow can be decomposed into finite invariant compact subsets and connecting ?orbits between them, which is helpful for us to study the inner structure of ?compact invariant sets. When dynamical systems are randomly perturbed, by real ?or white noise, we show that for finite and infinite dimensional random ?dynamical systems, we have the random Morse decomposition; we also construct ?Lyapunov function for the decomposition. For deterministic systems, we introduce ?the concept of natural order to study the relative stability of Morse sets by ?the stochastic perturbation method. We also investigate the stochastic stability ?of Morse (invariant) sets under general white noise perturbations when the ?intensity of noise converges to zero.