On the reducibility of 2-dimensional linear quasi-periodic systems with small parameters

Xu, Junxiang; Kun, Wang; Min, Zhu

doi:10.1090/proc/13088

On the reducibility of 2-dimensional linear quasi-periodic systems with small parameters
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by Junxiang Xu, Wang Kun and Zhu Min PDF

Proc. Amer. Math. Soc. 144 (2016), 4793-4805 Request permission

Abstract:

In this paper we consider a real analytic linear quasi-periodic system of 2-dimension, whose coefficient matrix depends on a small parameter $C^m$-smoothly and closes to constant. Under some non-resonance conditions about the basic frequencies and the eigenvalues of the constant matrix and without any non-degeneracy assumption with respect to the small parameter, we prove that the system is reducible for many of the sufficiently small parameters.

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