A newton-like method for computing normally hyperbolic invariant tori

Abstract

This chapter presents some ideas of normally hyperbolic manifold theory, and focuses on the algorithmic application of the parameterization method in such context. The parameterization method is applied to the computation of several normally hyperbolic invariant manifolds, in the following examples: computation of an attracting invariant curve in a 2D- Fattened Arnold Family, computation of a saddle invariant curve in a 3D- Fattened Arnold Family, and the computation of a 2D normally hyperbolic invariant cylinder in the Froeschlé map.