报告题目：On Small Noise Perturbations of Deterministic Dynamical Systems
报告人： 蒋继发 教授（上海师范大学）
报告时间：2019年11月23日（星期六）上午9:00-9:40
报告地点：创新园大厦 B1410
校内联系人：柳振鑫 教授 联系电话：84708351-8039
报告摘要: This talk presents a general framework to deal with the limit behavior of stationary measures for small noise perturbations of deterministic dynamical systems. Under the probability convergence assumption, we prove that any weak convergent limit of a sequence of stationary measures is an invariant measure of deterministic dynamical system, whose support is contained in the Birkhoff center of the deterministic dynamical system. This result can be applied to SODEs, SPDEs and SFDEs driven by either Brown motion or Levy process with small noise intensity as well as stochastic approximation with constant step. We also discuss stochastic stability and provide a criterion for a repeller to be a null set of limit measures for SODEs with small nondegenerate noise and prove that any limit cycle of a planar system with positive characteristic exponent is always a null set of limit measures. We show that there is a distinct difference on stochastic stability between noise perturbed systems of structurally stable and structurally unstable deterministic systems.
This is a joint work with Dr. Chen Lifeng and Profs. Dong Zhao and Zhai Jianliang.
大连理工大学数学科学学院
2019年11月20日
