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.