Invariant manifolds are landmarks that organize the long term behavior of dynamical systems with complicated trajectories. From the point of view of applications, it is interesting to know that they persist under perturbations or that one can validate the the numerical calculations finding them. There are two main theorems in this direction: Normal hyperbolicity and KAM theory. We will present numerical explorations and rigorous results on what happens on the boundary of validity of these theorems. There are some surprising regularities and scaling relations, some of which can be proved rigorously. This is joint work with many people including R. Calleja, A. Haro, T. Blass.
Manifolds on the verge of a regularity breakdown
Rafael de la Llave, Georgia Tech
Mar 2 2015 - 4:30pm