Georgia Institute of Technology College of Sciences

The Parameterization Method is a functional analytic framework for studying invariant manifolds such as stable/unstable manifolds of periodic orbits and invariant tori. This talk will focus on numerical applications such as computing manifolds associated with long periodic orbits, and computing periodic invariant circles (manifolds consisting of several disjoint circles mapping one to another, each of which has an iterate conjugate to an irrational rotation). I will also illustrate how to combine Automatic Differentiation with the Parameterization Method to simplify problems with non-polynomial nonlinearities.