Computer-Assisted Proofs of Existence of Invariant Tori in Quasi-periodic Systems via Fourier Methods

The goal of this paper is to provide a methodology to prove existence of (fiberwise hyperbolic) real-analytic invariant tori in real-analytic quasi-periodic skew-product dynamical systems that present nearly-invariant tori of the same characteristics. The methodology is based on the application of a Newton-Kantorovich theorem whose hypotheses are tested using Fourier analysis methods for a numerical approximation of the parameterization of an invariant torus.