Manifolds on the Verge of a Regularity Breakdown

Series
Research Horizons Seminar
Time
Wednesday, October 30, 2013 - 12:00pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Rafael de la Llave – School of Mathematics – rll6@math.gatech.eduhttp://people.math.gatech.edu/~rll6/
Organizer
Robert Rahm
In dynamical systems, the long term behavior is organized by invariant manifolds that serve as landmarks that organize the traffic. There are two main theorems (established around 40-60 years ago) that tell you that these manifolds persist under small perturbations: KAM theorem and the theory of normally hyperbolic manifolds. In recent times there have been constructive proofs of these results which also lead to effective algorithms which allow to explore what happens in the border of the applicability of the theorems. We plan to review the basic concepts and present the experimental results.