### Strongly dissipative systems with a quasi-periodic forcing term

- Series
- Math Physics Seminar
- Time
- Wednesday, October 24, 2018 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Guido Gentile – Universita di Roma 3 – gentile@mat.uniroma3.it

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.