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

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.
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/137665
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