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

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

Authors:	Email author" target="_blank">Ren?Zi?Yang Email author Jun?Xiang?Xu

Institution:	(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: $\ifmmode\expandafter\dot\else\expandafter\.\fi{x} = {\left( {A + {\user1{\varepsilon }}Q{\left( {t,{\user1{\varepsilon }}} \right)}} \right)}x,{\left\| {\user1{\varepsilon }} \right\|} \leqslant {\user1{\varepsilon }}_{0}$ , 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 $\ifmmode\expandafter\dot\else\expandafter\.\fi{y} = {\left( {A^{ * } {\left( {\user1{\varepsilon }} \right)} + R^{ * } {\left( {t,{\user1{\varepsilon }}} \right)}} \right)}y,{\left\| {\user1{\varepsilon }} \right\|} \leqslant {\user1{\varepsilon }}_{0}$ , where R* is exponentially small in ɛ.

Keywords:	Linear differential equations Effective reducibility Quasiperiodic
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