FM 13-2009 (mp_arc 09-184; arXiv:0910.0746 [math.DS])

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
UniversitÓ di Roma Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy
e-mail: gentile@mat.uniroma3.it