珠海数学杰出学者讲座第5讲-Stable and Chaotic Dynamics in Certain Quasi-periodically Forced Differential Equations

讲座时间 Datetime: 2022年11月8日，星期二，15:30-17:30

地点 Venue: 腾讯线上会议：473-858-834

主持人 Host：赵育林

报告人 Speaker: 吕克宁 

单位 Affiliation: 四川大学

报告摘要 Abstract:

We study the complicated dynamics of quasi-periodically perturbed ordinary differential equations with a homoclinic orbit to a dissipative saddle point. We show that there are four regions of parameters in which the equations have respectively: (1) attracting quasi-periodic integral manifolds of Levinson type; (2) transition to chaos; (3) strange attractors;(4) homoclinic tangles. In the case of homoclinic tangles, we not only obtain the results on horseshoes similar to the existing ones, but also give a comprehensive geometric description of the structures of tangles.

报告人简介：

吕克宁教授是微分方程与无穷维动力系统专家，曾任Brigham Young University和Michigan State University教授，现任四川大学教授，2017年获首届“张芷芬数学奖”，2020年入选AMS fellow，现任国际学术刊物JDE共同主编。他在不变流形和不变叶层，Sinai-Ruelle-Bowen测度，熵和Lyapunov指数以及随机动力系统的光滑共轭理论和随机偏微分方程的动力学方面做出了多个工作，相关论文发表在《Inventiones mathematicae》、《Communications on Pure and Applied Mathematics》、《Memoirs of the American Mathematical Society》等学术期刊上。