Domains of analyticity for response solutions in strongly dissipative forced systems

Journal Article · Sun Dec 15 00:00:00 EST 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4836777· OSTI ID:22251754

Corsi, Livia ^[1]; Feola, Roberto ^[2]; Gentile, Guido ^[3]

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1. Dipartimento di Matematica, Università di Napoli “Federico II,” Napoli I-80126 (Italy)
2. Dipartimento di Matematica, Università di Roma “La Sapienza,” Roma I-00185 (Italy)
3. Dipartimento di Matematica, Università di Roma Tre, Roma I-00146 (Italy)

We study the ordinary differential equation εx{sup ¨}+x{sup .}+εg(x)=εf(ωt), where g and f are real-analytic functions, with f quasi-periodic in t with frequency vector ω. If c{sub 0}∈R is such that g(c{sub 0}) equals the average of f and g′(c{sub 0}) ≠ 0, under very mild assumptions on ω there exists a quasi-periodic solution close to c{sub 0} 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.

• OSTI ID: 22251754
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTIC FUNCTIONS
DIFFERENTIAL EQUATIONS
MATHEMATICAL SOLUTIONS
PERIODICITY
VECTORS