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Morse decomposition for random dynamical systems
澳门新葡8455最新网站:2016年10月03日 08:32 点击数:

报告人:柳振鑫

报告地点:澳门新葡8455最新网站615室

报告澳门新葡8455最新网站:2016年10月04日星期二09:00-10:00

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报告摘要:

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, what we concern is if we can study the structure of an invariant random compact sets, including global random attractors? 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. By this, we may introduce the concept of random gradient system as a random semiflow possessing a continuous random Lyapunov function which describes the asymptotic behavior of the system. 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.

主讲人概况:

柳振鑫,大连理工大学数学科学新葡京最新官网教授,优秀青年科学基金获得者,主持了多项国家自然科学基金。他的主要研究方向为随机动力系统,在Ann. Probab.,J. Funct. Anal.,SIAM J. Appl. Dyn. Syst.,Nonlinearity,J. Differential Equations等国际期刊上发表学术论文20多篇。

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