Livia Corsi and Guido Gentile
Resonant tori of arbitrary codimension for quasi-periodically forced systems
(395K, pdf)
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.