FM 02-14 (arXiv:1403.2872)

Author: Livia Corsi and Guido Gentile

Title: Resonant tori of arbitrary codimension for quasi-periodically forced systems
 
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.

Keywords: Lower-dimensional tori; quasi-periodic solutions; forced systems; non-degeneracy; Bryuno condition; time-reversible systems.

Livia Corsi
Dipartimento di Matematica
Università di Roma "La Sapienza"
P.le Aldo Moro 5, 00195 Roma, Italy
e-mail: livia.corsi@unina.it

Guido Gentile
Dipartimento di Matematica e Fisica
Università Roma Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy
e-mail: gentile@mat.uniroma3.it