KAM theory for the reversible perturbations of 2D linear beam equations

被引：7

作者：

Ge, Chuanfang ^{[1
]}

Geng, Jiansheng ^{[1
]}

Lou, Zhaowei ^{[2
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

[2] Nanjing Univ Aeronaut & Astronaut, Coll Sci, Nanjing 211106, Peoples R China

来源：

MATHEMATISCHE ZEITSCHRIFT | 2021年 / 297卷 / 3-4期

基金：

中国国家自然科学基金;

关键词：

KAM theory; Reversible vector field; Beam equation; Quasi-periodic solutions; Birkhoff normal form; QUASI-PERIODIC SOLUTIONS; PARTIAL-DIFFERENTIAL-EQUATIONS; REDUCIBILITY; TORI;

D O I：

10.1007/s00209-020-02575-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper, we prove an infinite dimensional reversible Kolmogorov-Arnold-Moser (KAM) theorem. As an application, we study the existence of KAM tori for a class of two dimensional (2D) non-Hamiltonian completely resonant beam equations with derivative nonlinearities. The Birkhoff normal form theory is also used since there are no external parameters in the equations.

引用

页码：1693 / 1731

页数：39

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