**Author:**
Guido Gentile

**Title:** *
Construction of quasi-periodic response solutions
in forced strongly dissipative systems
*

**Abstract: **
We consider a class of ordinary differential equations describing
one-dimensional quasiperiodically forced systems in the presence
of large damping. We give a fully constructive proof of the existence
of response solutions, that is quasi-periodic solutions which have the
same frequency vector as the forcing. This requires dealing with a
degenerate implicit function equation: we prove that the latter has
a unique solution, which can be explicitly determined. As a by-product
we obtain an explicit estimate of the minimal size of the damping
coefficient.

**Keywords:**
Dissipative systems; Periodically forced systems;
Quasi-periodically forced systems; Lindstedt series;
Renormalization group; Divergent series; Bryuno vectors.

Guido Gentile

Dipartimento di Matematica

Università di Roma Tre

Largo San Leonardo Murialdo 1, 00146 Roma, Italy

e-mail: gentile@mat.uniroma3.it