FM 010-2012 (arXiv:1210.3998; mp_arc 12-120)

Author: Livia Corsi, Roberto Feola and Guido Gentile

Title: Domains of analyticity for response solutions in strongly dissipative forced systems
 
Abstract: We study the ordinary differential equation ε x'' + x' + ε g(x) = ε f(ω t), where g and f are real-analytic functions, with f quasi-periodic in t with frequency vector ω. If c0R is such that g(c0) equals the average of f and g'(c0) ≠ 0, under very mild assumptions on ω there exists a quasi-periodic solution close to c0 with the frequency vector ω. We show that such a solution depends analytically on ε in a domain of the complex plane tangent more than quadratically to the imaginary axis at the origin.

Keywords: Strongly dissipative systems, quasi-periodic forcing, quasi-periodic solutions, analyticity domain, asymptotic expansion.

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 Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy
e-mail: roberto_feola@hotmail.com

Guido Gentile
Dipartimento di Matematica
Università di Roma Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy
e-mail: gentile@mat.uniroma3.it