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arXiv · 2403.18566

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

Alex Haro·Eric Sandin Vidal
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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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Alex Haro, Eric Sandin Vidal. 2024-03-27. Computer-Assisted Proofs of Existence of Invariant Tori in Quasi-periodic Systems via Fourier Methods. https://doi.org/10.3934/dcdsb.2024143

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