拟周期系统的Floquet理论 |
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引用本文: | 林振声. 拟周期系统的Floquet理论[J]. 应用数学和力学, 1982, 3(3): 327-344 |
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作者姓名: | 林振声 |
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作者单位: | 福州大学数学系 |
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摘 要: | 在这篇文章,我们对拟周期系统dx/dt=A(ω1t,ω2t.…,ωmt)x (0.1)建立了Floquet理论.其中n×n方阵A(u1,u2,…,um)是u1,u2,…,um以2π为周期的周期方阵,同时假定A(u1,u2,…,um)∈Cτ,τ=(N+1)τ0,τ0=2(m+1),N=1/2n(n+1).我们定义了(0.1)的特征指数根β1,β2,…,βn,假设下式成立:其中K(ω),K(ω,β)>0,kμ,iv是整数,k1,k2…,km不全为零:i2=-1.那末有拟周期线性变换,把(0.1)化为常系数的线性系统.
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收稿时间: | 1981-10-06 |
The Floquet Theory for Quasi-Periodic Linear System |
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Affiliation: | Department of Mathematics, Fuzhou University, Fuzhou |
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Abstract: | In this paper we establish the Floguet theory for the quasi-periodic system where A(u1,u2...um) is an nxn periodic matrix function ofwith period 2π, and it is of Cτ, τ=(N+1)τ0, τ0=2(m+1), N = (1/2)n(n+l).Meanwhile, we define the characteristic exponential roots β1,β2,…,βn of (0.1), and assume that where K(ω), K(ω,β)->0. ku, iv, are integers, all the integers k1,k2,…,km,km are not zero, ,rhen therequasi-periodic linear transformation, which carries (0.1) into a linear system with constant coefficients. |
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