报告题目：Stochastic Stability of Invariant Measures for Quasipotential Systems

报告时间：2023-11-06   16:00-17:00

报 告 人 ：蒋继发  教授  上海师范大学

报告地点：理学院东北楼四楼学术报告厅（404）

Abstract： A smooth vector field, called quasipotential, can be generically decomposed into the sum of a gradient vector field and a divergence-free vector field. This talk first gives the sufficient and necessary condition for a system to be quasipotentialand then presents the criteria for invariant measures to be stochastically stable under additive noise perturbation by the Laplace method. It is proved that limiting measures of stationary measures concentrate on the global minima set of the potential function. The Laplace method will determine the weights on components of the global minima set, which gives the stochastically stable invariant measures. The supports of stochastically stable invariant measures contain either Lyapunov stable equilibria, or saddles, or periodic orbits, or quasiperiodic orbits or heteroclinic orbits, or even chaotic motions, while the most existing results are on gradient systems, supports of their stochastically stable invariant measures only contain Lyapunov stable equilibria. We also provide the method how to explicitly compute the transition difficulty matrix between limit sets by uniform large deviation principles, which again determines the stochastically stable invariant measures.