A KAM THEOREM FOR DEGENERATE INFINITE-DIMENSIONAL REVERSIBLE SYSTEMS

被引：0

作者：

Lou, Zhaowei ^{[1
]}

Wu, Youchao ^{[1
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Sch Math, Nanjing 211106, Peoples R China

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 2024卷 / 02期

基金：

中国国家自然科学基金;

关键词：

KAM theorem; infinite-dimensional reversible system; Russmann non-degeneracy condition; QUASI-PERIODIC SOLUTIONS; INVARIANT TORI; PERTURBATIONS; PERSISTENCE;

D O I：

10.58997/ejde.2024.02

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we establish a Kolmogorov-Arnold-Moser (KAM) theorem for degenerate infinite-dimensional reversible systems under a non degenerate condition of Ru center dot ssmann type. This theorem broadens the scope of applicability of degenerate KAM theory, previously confined to Hamiltonian systems, by incorporating infinite-dimensional reversible systems. Using this theorem, we obtain the existence and linear stability of quasi-periodic solutions for a class of non-Hamiltonian but reversible beam equations with non-linearities in derivatives.

引用

页数：20

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