On the reducibility of linear differential equations with quasiperiodic coefficients
On the reducibility of linear differential equations with quasiperiodic coefficients
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DOI：
10.1016/0022-0396(92)90107-x
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发表时间：
1992-07
影响因子：
2.4
通讯作者：
À. Jorba;C. Simó
中科院分区：
文献类型：
--
作者：
À. Jorba;C. Simó
考虑Rd中的系统x今=（A+ εQ（t））x，其中A为常数矩阵，Q为具有r个基频的拟周期解析矩阵. A的特征值是任意的，包括纯虚的情况。假设由A的本征值和Q的基频构成的集合满足非共振条件。然后存在一个正测度Cantorian集E，使得对于ε <$E，只要非退化条件成立，系统可以通过变量的拟周期变化约化为常系数。该条件防止在谐振时锁定。
The system x ̇=(A+ εQ (t)) x in R d is considered, where A is a constant matrix and Q a quasiperiodic analytic matrix with r basic frequencies. The eigenvalues of A are arbitrary including the purely imaginary case. Suppose that the set formed by the eigenvalues of A and the basic frequencies of Q satisfies a nonresonant condition. Then there is a positive measure cantorian set E such that for ε ϵ E the system is reducible to constant coefficients by means of a quasiperiodic change of variables, provided a nondegeneracy condition holds. This condition prevents locking at resonance.