Effective Reducibility of a Class of Linear Differential Equations with Quasiperiodic Coefficients期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Effective Reducibility of a Class of Linear Differential Equations with Quasiperiodic Coefficients

Authors:	Ren?Zi?Yang author-information" > author-information__contact u-icon-before" > mailto:yrz@seu.edu.cn" title=" yrz@seu.edu.cn" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Jun?Xiang?Xu

Affiliation:	(1) Department of Mathematics, Southeast University, Nanjing, 210018, P. R. China

Abstract:	Abstract In this paper we consider the effective reducibility of the following linear differential equation: $ifmmodeexpandafterdotelseexpandafter.fi{x} = {left( {A + {user1{varepsilon }}Q{left( {t,{user1{varepsilon }}} right)}} right)}x,{left\| {user1{varepsilon }} right\|} leqslant {user1{varepsilon }}_{0}$ , where A is a constant matrix, Q(t,ɛ) is quasiperiodic in t, and ɛ is a small perturbation parameter. We prove that if the eigenvalues of A and the basic frequencies of Q satisfy some non-resonant conditions, the linear differential equation can be reduced to $ifmmodeexpandafterdotelseexpandafter.fi{y} = {left( {A^{ * } {left( {user1{varepsilon }} right)} + R^{ * } {left( {t,{user1{varepsilon }}} right)}} right)}y,{left\| {user1{varepsilon }} right\|} leqslant {user1{varepsilon }}_{0}$ , where R* is exponentially small in ɛ.

Keywords:	Linear differential equations Effective reducibility Quasiperiodic
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