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arXiv · 0910.0746

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

Guido Gentile
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Abstract

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

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Guido Gentile. 2009-10-05. Construction of quasi-periodic response solutions in forced strongly dissipative systems. https://arxiv.org/abs/0910.0746

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