摘要
本文研究了如下系统{(x)=ω+y+f(x,y),(y)=g(x,y)的不变环面的保持性问题,其中x ∈ T^(Λ),y ∈ R^(Λ),集合Λ是整数集合Z的可数子集,频率ω=(…,ωλ,…)λ∈Λ ∈ R^(Λ)是双边无穷有理不相关序列,也就是说,频率ω=(...,ωλ的任意有限部分都有理不相关,扰动项f,g是实解析函数.我们还假设上述系统关于对合M:(x,y)(→)(-x,y)是可逆的.由KAM方法,证明了上述无穷维可逆系统的不变环面的保持性.
In this paper,we consider the persistence of invariant tori in the following system{(x)=ω+y+f(x,y),(y)=g(x,y),where x∈T^(Λ),y∈RΛ,Λis a countable subset of Z,ω=(…,ωλ,...)λ∈Λ∈RΛis the frequency vector,ω=(…,ωλ,…)λ∈Λis a bilateral infinite sequence of rationally independent frequency,in other words,any finite segments ofω=(…,ωλ,…)λ∈Λare rationally independent,and the perturbations f,g are real analytic functions.We also assume that the above system is reversible with respect to the involution M:(x,y)(→)(-x,y).By the KAM method,we prove the persistence of invariant tori for the above reversible system.
作者
黄鹏
Peng HUANG(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,P.R.China)
出处
《数学学报(中文版)》
CSCD
北大核心
2024年第6期1207-1220,共14页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金(12261014,11901131)。
关键词
不变环面
KAM理论
无穷维可逆系统
invariant tori
KAM theory
infinite dimensional reversible system