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Extension of Floquets theory to nonl

时间:2021-12-11 15:45:28 数理化学论文 我要投稿

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   作者单位: School of Mathematical Sciences,Peking University,Beijing 100871,China  刊 名: 中国科学A辑(英文版)  SCI 英文刊名: SCIENCE IN CHINA SERIES A (MATHEMATICS)  年,卷(期): 2005 48(12)  分类号: O1  关键词: quasiperiodic system   normal form