Parameterization method for computing quasi-periodic reducible normally hyperbolic invariant tori

Abstract

We consider the problem of numerically computing quasi-periodic normally hyperbolic invariant tori (NHIT) with fixed frequency as well as their invariant bundles. The algorithm is based on a KAMscheme to find the parameterization of a torus with fixed Diophantine frequency (by adjusting parameters of the model), and suitable Floquet transformations that reduce the linearized dynamics to constant coefficients. We apply this method to continue curves of quasi-periodic NHIT of a perturbed dynamical system and to explore the mechanism of breakdown of these invariant tori. We observe in these continuations that the invariant bundles may collide even if the Lyapunov multipliers remain separated.