- 10-181 Livia Corsi and Guido Gentile
- Response solutions for arbitrary quasi-periodic
perturbations with Bryuno frequency vector
Nov 3, 10
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Abstract. We study the problem of existence of response solutions for a
real-analytic one-dimensional 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 exploit the formal analogy
with problems of quantum field theory; a crucial role is played by
remarkable identities between classes of diagrams.