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On the Kolmogorov theorem for some infinite-dimensional Hamiltonian systems of short range
Nonlinear Analysis ( IF 1.3 ) Pub Date : 2020-09-19 , DOI: 10.1016/j.na.2020.112120 Yuan Wu , Xiaoping Yuan
中文翻译:
关于一些短范围无限维哈密顿系统的Kolmogorov定理
更新日期:2020-09-20
Nonlinear Analysis ( IF 1.3 ) Pub Date : 2020-09-19 , DOI: 10.1016/j.na.2020.112120 Yuan Wu , Xiaoping Yuan
In this paper, it is proved that the infinite KAM torus with prescribed frequency exists in a sufficiently small neighbourhood of a given for nearly integrable and analytic Hamiltonian system of infinite degree of freedom and of short range. That is to say, we will give an extension of the original Kolmogorov theorem to the infinite-dimensional case of short range. The proof is based on the approximation of finite-dimensional Kolmogorov theorem and an improved KAM machinery which works for the normal form depending only on initial .
中文翻译:
关于一些短范围无限维哈密顿系统的Kolmogorov定理
在本文中,证明了给定频率的无限KAM圆环存在于给定的足够小的邻域中 用于几乎可积分和解析的哈密顿系统 具有无限的自由度和短距离。也就是说,我们将原始的Kolmogorov定理扩展到短距离的无穷维情况。该证明是基于有限维Kolmogorov定理的近似值和一种改进的KAM机器,该机器仅以初始形式为标准形式工作。