Invariant Manifolds and Singularly Perturbed Equations (IP8)

IP8 ~ Tuesday, May 23, 1995 ~ 1:30 PM

Invariant Manifolds and Singularly Perturbed Equations

Singularly perturbed equations often have "singular solutions", which are unions of solutions to limiting equations. A very general and central question, to which there have been many approaches, is what hypotheses on the equations and singular solutions guarantee that the singular solutions approximate some solutions for the e > 0 problem. The speaker will present a geometric approach to the problem based on the "Exchange Lemma", which gives estimates on the position of an invariant manifold and its tangent planes as the manifold passes close to a normally hyperbolic piece of a slow manifold.

Nancy Kopell
Department of Mathematics, Boston University

3/15/95