Extension of Floquets theory to nonlinear quasiperiodic differential equations
In this paper, we consider the following autonomous system of differential equations:(x) = Ax + f(x, θ), (θ) = ω,where θ∈ Rm, ω = (ω1,...,ωm) ∈ Rm, x ∈ Rn, A ∈ Rn×n is a constant matrix and is hyperbolic, f is a C∞ function in both variables and 2π-periodic in each component of the vector θ which satisfies f = O(‖x‖2) as x → 0. We study the normal form of this system and prove that under some proper conditions this system can be transformed to an autonomous system:(x) = Ax + g(x), (θ) = ω.Additionally, the proof of this paper naturally implies the extension of Chen's theory in the quasi-periodic case.
作 者： WU Hao LI Weigu 作者單位： School of Mathematical Sciences,Peking University,Beijing 100871,China 刊 名： 中國科學A輯（英文版） SCI 英文刊名： SCIENCE IN CHINA SERIES A (MATHEMATICS) 年，卷(期)： 2005 48(12) 分類號： O1 關鍵詞： quasiperiodic system normal form【Extension of Floquets theory to nonl】相關文章：
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