This talk contains three parts: (1) Lyapunov exponents for infinite dimensional dynamical systems; (2) the existence of SRB measures and their properties for infinite dimensional dynamical systems and SRB measures for parabolic PDEs undergoing Hopf bifurcations driven by a periodic forcing with applications to the Brusselator; (3) Positive entropy implying the existence of horseshoes for infinite dimensional dynamical systems. This is based on the joint works with Wen Huang,Zeng Lian, Peidong Liu, Qiudong Wang, and Lai-Sang Young.
简介👋🏿：吕克宁，美国杨伯翰大学数学系教授🙆🏼♀️⛹🏿♂️。1982年毕业于四川大学数学系，1988年毕业于美国密西根州立大学👨👩👧👧⚧，获博士学位。研究方向为无穷维动力系统及非线性偏微分方程。从1992年以来连续获得美国国家自然科学基金资助👩💻，曾获杰青年（B类）、入选QR计划等🧏🏿♂️。多次应邀在重要的国际学术会议上作大会报告，美国《J. Differential Equations》等国际著名学术期刊编委，在世界数学一流杂志《Invent. Math.》、《Communications on Pure and Applied Mathematics》、《Memoirs of AMS》等上发表多篇研究论文。
