Response solutions for arbitrary quasi-periodic perturbations with Bryuno frequency vector
Livia Corsi,
Guido Gentile
Abstract:We study the problem of existence of response solutions for a real-analytic onedimensional system, consisting of a rotator subjected to a small quasi-periodic forcing. We prove that at least one response solution always exists, without any assumption on the forcing besides smallness and analyticity. This strengthens the results available in the literature, where generic non-degeneracy conditions are assumed. The proof is based on a diagrammatic formalism and relies on renormalisation group techniques, which ex… Show more
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