Morse decomposition for random dynamical systems


主讲人:柳振鑫 大连理工大学教授 博士生导师





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.