| Effective Reducibility of a Class of Linear Differential Equations with Quasiperiodic Coefficients |
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| 作者姓名： | RenZiYANG JunXiangXU |
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| 作者单位： | DepartmentofMathematics,SoutheastUniversity,Nanjing210018,P.R.China |
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| 摘 要： | In this paper we consider the effective reducibility of the following linear differentialequation: x = (A ∈Q(t,∈))x, |∈| ≤ ∈0, where A is a constant matrix, Q(t,e) is quasiperiodic in t, and e 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 y = (A^*(∈) R^*(t, ∈))y, |∈| ≤ ∈o, where R^* is exponentially small in ∈.
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| 关 键 词： | 线性微分方程 有效还原性 准周期性 时滞方程 |
| 收稿时间： | 7 March 2001 |
Effective Reducibility of a Class of Linear Differential Equations with Quasiperiodic Coefficients |
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| RenZiYANG JunXiangXU.Effective Reducibility of a Class of Linear Differential Equations with Quasiperiodic Coefficients[J].Acta Mathematica Sinica,2004,20(3):525-532. |
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| Authors: | Email author" target="_blank">Ren?Zi?YangEmail author Jun?Xiang?Xu |
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| Institution: | (1) Department of Mathematics, Southeast University, Nanjing, 210018, P. R. China |
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| Abstract: | Abstract
In this paper we consider the effective reducibility of the following linear differential equation:
, 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
, where R* is exponentially small in ɛ. |
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| Keywords: | Linear differential equations Effective reducibility Quasiperiodic |
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