Morse decomposition for random dynamical systems

[TMCSC]

July 05, 2019  16:30-18:00

四川大学东三教学楼 247

[lecture]0705Zhenxin Liu-01.jpg

SPEAKER

柳振鑫（大连理工大学）

ABSTRACT

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.

ORGANIZERS

洪绍方（四川大学）

寇     辉（四川大学）

连     增（四川大学）

SUPPORTED BY

国家天元数学西南中心

四川大学数学学院