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Morse decomposition for random dynamical systems

發布者:文明辦發布時間:2019-06-27瀏覽次數:142


主講人:柳振鑫 大連理工大學教授 博士生導師


時間:2019年7月3日13:00


地點:3號樓301室


舉辦單位:數理學院


主講人介紹:柳振鑫,大連理工大學數學科學學院教授、博士生導師。主要從事隨機動力系統的研究;在隨機Conley指標理論、隨機回復運動、平穩分布等方面做出系統深入的研究工作。


內容介紹: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.

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