10-185 J.Ll Figueras, A. Haro

Computer Assisted Proofs of existence of Fiberwise Hyperbolic Invariant Tori in skew products over rigid rotations (4692K, pdflatex) Nov 18, 10

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Abstract. We present a methodology to perform Computer Assisted Proofs for the existence and (local) uniqueness of Fiberwise Hyperbolic Invariant Tori in skew product systems over rotations. The theoretical basis is a tailored version of the Newton-Kantorovich theorem for the functional equations describing the invariance of tori and their stable and unstable subbundles. The computational tools allow the rigorous manipulation of truncated Fourier series, which parametrize the tori and their subbundles used in the validations. Our methodology exploits the special form of these dynamical systems, and it is based on the results exposed on the papers by Haro and de la Llave, 2006, 2007. We apply these techniques to two scenarios where the invariant tori are on the verge of hyperbolicity breakdown.

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