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

2024/03/27 by Haro, Alex, Vidal, Eric Sandin
#37C55 #37C60 #37D10 #42A16 #65G30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.18566

Abstract

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.

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