无穷维可逆系统的不变环面的保持性  

Persistence of Invariant Tori in Infinite Dimensional Reversible Systems

作　　者：黄鹏 Peng HUANG(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,P.R.China)

机构地区：[1]贵州财经大学数学与统计学院,贵阳550025

出　　处：《数学学报（中文版）》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)。

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.

关 键 词：不变环面 KAM理论 无穷维可逆系统 

分 类 号：O175.1[理学—数学]