Computer assisted proofs for normally hyperbolic invariant manifolds

CDSNS Colloquium
Monday, August 27, 2012 - 11:00am
1 hour (actually 50 minutes)
Skiles 06
AGH Univ. Krakow and SOM, Gatech
We shall present a method which establishes existence of normally hyperbolic invariant manifolds for maps within a specified domain. The method can be applied in a non-perturbative setting. The required conditions follow from bounds on the first derivative of the map, and are verifiable using rigorous numerics. We show how the method can be applied for a driven logistic map, and also present examples of proofs of invariant manifolds in the restricted three body problem.