Wednesday, August 9

Invariant Manifolds for Infinite Dimensional Dynamical Systems

11:00 AM-11:50 AM
Koali (Salon 5)
Chair: Shui-Nee Chow, National University of Singapore, Singapore; and Georgia Institute of Technology, USA

The investigation of a particular dynamical system or a family of dynamical systems usually can be traced to an evolving physical system whose behavior one would like to understand and possibly predict. And so one of the main goals of the study of dynamical systems is to understand the long term behavior of states in the systems. To have a better understanding of the physical phenomena being modeled, one needs to investigate not only the mathematical model but also the perturbations of the model. One also needs to study how the qualitative properties of the perturbed models are related to the qualitative properties of the original model. This leads to the fundamental problem of the existence and the persistence of invariant manifolds under perturbation and to the study of the qualitative properties of the flow near invariant manifolds

In this presentation, the speaker will report some recent works on the existence and persistence of normally hyperbolic invariant manifolds and invariant foliations for infinite dimensional dynamical systems. He will also report on recent work on approximated normally hyperbolic invariant manifolds. This is a joint work with Peter Bates and Chongchun Zeng.

Kening Lu
Department of Mathematics
Brigham Young University, USA
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