A Formal KAM Theorem for Hamiltonian Systems and Its Application to Hyperbolic Lower Dimensional Invariant Tori

被引：0

作者：

Li, Qi ^{[1
]}

Xu, Junxiang ^{[1
]}

机构：

[1] Southeast Univ, Dept Math, Nanjing 210096, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2024年 / 23卷 / 02期

关键词：

Formal KAM theorem; Bruno-Russmann condition; KAM iteration; CONSERVATION; PERSISTENCE; FREQUENCIES;

D O I：

10.1007/s12346-023-00938-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we reformulate a formal KAM theorem for Hamiltonian systems with parameters under Bruno-Russmann condition. The proof is based on KAM iteration and the key is to adjust the parameters for small divisors after KAM iteration instead of in each KAM step. By this formal KAM theorem we can follow some well known KAM-type results for hyperbolic tori. Moreover, it can also be applied to the persistence of invariant tori with prescribed frequencies.

引用

页数：23

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