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(guó)科學(xué)A輯（英文版）  SCI 英文刊名： SCIENCE IN CHINA SERIES A (MATHEMATICS)  年，卷(期)： 2005 48(12)  分類(lèi)號(hào)： O1  關(guān)鍵詞： quasiperiodic system   normal form  

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