On reducibility for a class of n-dimensional quasi-periodic systems with a small parameter

Yuedong Kong, Xuezhu Lu and Yanling Shi

Applied Mathematics and Computation, 2015, vol. 264, issue C, 272-278

Abstract: In this paper we consider the reducibility of a class of n-dimensional real analytic quasi-periodic systems with a small parameter: x˙=(A+ϵQ(t,ϵ))x,x∈Rn.We prove that if the basic frequencies of Q and the eigenvalues of A satisfy some non-resonance conditions, then for most of the sufficiently small parameters in the sense of Lebesgue measure, the system is reducible without any non-degeneracy assumption with respect to the parameter. Moreover, under some assumptions, we obtain a similar result for nonlinear quasi-periodic systems.

Keywords: Reducibility; Quasi-periodic perturbation; Non-degeneracy condition; KAM theory (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:264:y:2015:i:c:p:272-278

DOI: 10.1016/j.amc.2015.04.108

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