Normally Elliptic Singular Perturbation Problems: Local Invariant Manifolds and Applications

Dissertation Defense
Monday, May 16, 2011 - 11:00am for 1 hour (actually 50 minutes)
Skiles 005
Nan Lu – School of Mathematics, Georgia Tech
Nan Lu

Please Note: Advisor Chongchun Zeng

We study the normally elliptic singular perturbation problems including both finite and infinite dimensional cases, which could also be nonautonomous. In particular, we establish the existence and smoothness of O(1) local invariant manifolds and provide various estimates which are independent of small singular parameters. We also use our results on local invariant manifolds to study the persistence of homoclinic solutions under weakly dissipative and conservative perturbations.