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arXiv · 1403.2872

Resonant tori of arbitrary codimension for quasi-periodically forced systems

Livia Corsi·Guido Gentile
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Abstract

We consider a system of rotators subject to a small quasi-periodic forcing. We require the forcing to be analytic and satisfy a time-reversibility property and we assume its frequency vector to be Bryuno. Then we prove that, without imposing any non-degeneracy condition on the forcing, there exists at least one quasi-periodic solution with the same frequency vector as the forcing. The result can be interpreted as a theorem of persistence of lower-dimensional tori of arbitrary codimension in degenerate cases.

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Livia Corsi, Guido Gentile. 2014-03-12. Resonant tori of arbitrary codimension for quasi-periodically forced systems. https://arxiv.org/abs/1403.2872

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