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On the reducibility of two-dimensional linear quasi-periodic systems with small parameter

Published online by Cambridge University Press:  04 August 2014

JUNXIANG XU  and
XUEZHU LU
JUNXIANG XU
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, PR China email xujun@seu.edu.cn, jennysundate@gmail.com
XUEZHU LU
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, PR China email xujun@seu.edu.cn, jennysundate@gmail.com
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Abstract

In this paper we consider a linear real analytic quasi-periodic system of two differential equations, whose coefficient matrix analytically depends on a small parameter 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 of the small parameter, we prove that the system is reducible for most of the sufficiently small parameters in the sense of the Lebesgue measure.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 7 , October 2015 , pp. 2334 - 2352
Copyright
© Cambridge University Press, 2014 

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