**Author:**
Livia Corsi, Roberto Feola and Guido Gentile

**Title:** *
Convergent series for quasi-periodically forced strongly dissipative systems
*

**Abstract: **
We study the ordinary differential equation
*ε x'' + x' + ε g(x) = ε f(ω t)*,
with *f* and *g* analytic and *f* quasi-periodic in *t*
with frequency vector *ω ∈ R^{d}*.
We show that if there exists

**Keywords:**
Strongly dissipative systems,
quasi-periodic forcing,
quasi-periodic solutions,
asymptotic expansion,
non-degeneracy,
irrationality conditions.

Livia Corsi

Dipartimento di Matematica

Università di Napoli "Federico II"

Monte Sant'Angelo, Via Cinthia, 80126 Napoli, Italy

e-mail: livia.corsi@unina.it

Roberto Feola

Dipartimento di Matematica

Università di Roma "La Sapienza"

Piazzale Aldo Moro 5, 00185 Roma, Italy

e-mail: feola@mat.uniroma1.it

Guido Gentile

Dipartimento di Matematica

Università di Roma Tre

Largo San Leonardo Murialdo 1, 00146 Roma, Italy

e-mail: gentile@mat.uniroma3.it