KAM theory for volume-preserving maps

Series: 
CDSNS Colloquium
Wednesday, August 14, 2013 - 15:30
1 hour (actually 50 minutes)
Location: 
Skiles 269 (Tentative)
,  
Carnegie Mellon
Organizer: 
I will present a KAM theorem on the existence of codimension-one invariant tori with Diophantine rotation vector for volume-preserving maps. This is an a posteriori result, stating that if there exists an approximately invariant torus that satisfies some non-degeneracy conditions, then there is a true invariant torus near the approximate one. Thus, the theorem can be applied to systems that are not close to integrable. The method of proof provides an efficient algorithm for numerically computing the invariant tori which has been implemented by A. Fox and J. Meiss. This is joint work with Rafael de la Llave.