Computation of normally hyperbolic invariant manifolds

Applied and Computational Mathematics Seminar
Monday, September 8, 2014 - 14:00
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech Mathematics
We explain a method for the computation of normally hyperbolic invariant manifolds (NHIM) in discrete dynamical systems.The method is based in finding a parameterization for the manifold formulating a functional equation. We solve the invariance equation using a Newton-like method taking advantage of the dynamics and the geometry of the invariant manifold and its invariant bundles.  The method allows us to compute a NHIM and its internal dynamics, which is a-priori unknown.We implement this method to continue the invariant manifold with respect to parameters, and to explore different mechanisms of breakdown.  This is a joint work with Alex Haro.