Strongly dissipative systems with a quasi-periodic forcing term

Math Physics Seminar
Wednesday, October 24, 2018 - 4:00pm for 1 hour (actually 50 minutes)
Skiles 005
Guido Gentile – Universita di Roma 3 –
Federico Bonetto
We consider a class of singular ordinary differential equations, describing systems subject to a quasi-periodic forcing term and in the presence of large dissipation, and study the existence of quasi-periodic solutions with the same frequency vector as the forcing term. Let A be the inverse of the dissipation coefficient. More or less strong non-resonance conditions on the frequency assure different regularity in the dependence on the parameter A: by requiring a non-degeneracy condition on the forcing term, smoothness and analyticity, and even Borel-summability, follow if suitable Diophantine conditions are assumed, while, without assuming any condition, in general no more than a continuous dependence on A is obtained. We investigate the possibility of weakening the non-degeneracy condition and still obtaining a solution for arbitrary frequencies.