Response Solutions of Degenerate Quasi-Periodic Systems Under Small Perturbations

被引：0

作者：

Ni, Song ^{[1
]}

Xu, Junxiang ^{[1
]}

机构：

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

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2023年 / 22卷 / 02期

关键词：

Quasi-periodic system; KAM-iteration; Degenerate equilibrium point; INVARIANT TORI; REDUCIBILITY;

D O I：

10.1007/s12346-023-00770-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper considers a class of n-dimensional degenerate systems with a quasi-periodic perturbation whose frequency is a diophantine vector. Assume that the unperturbed system has the origin as an equilibrium, which is degenerate at one direction. By KAM iteration, we prove that the perturbed quasi-periodic system has a small response solution for sufficiently small perturbations. The proof is based on the idea of reducibility and the KAM technique of introducing parameters.

引用

页数：24

共 20 条

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