报告题目：Morse decomposition for random dynamical systems
报告时间：2019年12月06日16:00
报告地点：永利体育官网登录3401
报告人：柳振鑫教授大连理工大学
摘要: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.
个人简介：柳振鑫，大连理工大学数学科学学院教授、博士生导师，国家杰出青年基金获得者。主要从事随机动力系统的研究，在随机Conley指标理论、随机动力系统中的回复性和稳定性、随机微分方程的平稳分布及Kolmogorov平稳分布极限问题等方面做出系统深入的研究工作。目前已在国内外有重要影响的杂志上发表学术论文30余篇。2010年获全国百篇优秀博士学位论文提名奖；2015年获得国家优秀青年科学基金资助;2019年获得国家杰出青年科学基金资助。
