  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.
