Resonant tori of arbitrary codimension for quasi-periodically forced systems

Math Physics Seminar
Thursday, March 5, 2020 - 4:00pm for 1 hour (actually 50 minutes)
Skiles 005
Guido Gentile – Universita' di Roma 3 –
Federico Bonetto

Consider a system of rotators subject to a small quasi-periodic forcing which (1) is analytic, (2) satisfies a time-reversibility property, and (3) has a Bryuno frequency vector. Without imposing any non-degeneracy condition, we prove that 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. This is a joint work with Livia Corsi.