Normally Elliptic Singular Perturbation Problems: Local Invariant Manifolds and Applications

Series: 
Dissertation Defense
Monday, May 16, 2011 - 11:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
School of Mathematics, Georgia Tech

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.