We consider a class of ordinary differential equations describing one-dimensional quasi-periodically 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.

Gentile, G. (2012). Construction of quasi-periodic response solutions in forced strongly dissipative systems. FORUM MATHEMATICUM, 24(4), 791-808 [10.1515/FORM.2011.084].

Construction of quasi-periodic response solutions in forced strongly dissipative systems

GENTILE, Guido
2012-01-01

Abstract

We consider a class of ordinary differential equations describing one-dimensional quasi-periodically 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.
2012
Gentile, G. (2012). Construction of quasi-periodic response solutions in forced strongly dissipative systems. FORUM MATHEMATICUM, 24(4), 791-808 [10.1515/FORM.2011.084].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/141195
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