We study the ordinary differential equation εx ̈ + x ̇ + εg(x) = εf (ωt), where g and f are real-analytic functions, with f quasi-periodic in t with frequency vector ω. If c0 ∈ R 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 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.
Corsi, L., Feola, R., Gentile, G. (2013). Domains of analyticity for response solutions in strongly dissipative forced systems. JOURNAL OF MATHEMATICAL PHYSICS, 54(12), 122701 [10.1063/1.4836777].
Domains of analyticity for response solutions in strongly dissipative forced systems
CORSI L;FEOLA R;GENTILE, Guido
2013-01-01
Abstract
We study the ordinary differential equation εx ̈ + x ̇ + εg(x) = εf (ωt), where g and f are real-analytic functions, with f quasi-periodic in t with frequency vector ω. If c0 ∈ R 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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
