Response solutions of 2-dimensional degenerate systems under quasi-periodic perturbations

被引：2

作者：

Ma, Zhichao ^{[1
,2
]}

Qu, Ru ^{[1
]}

Xu, Junxiang ^{[1
]}

机构：

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

[2] Nanjing Forestry Univ, Coll Sci, Nanjing 210037, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 360卷

基金：

中国国家自然科学基金;

关键词：

Quasi-periodic system; Degenerate equilibrium point; KAM iteration; Response solution; TORI;

D O I：

10.1016/j.jde.2023.03.046

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper considers quasi-periodic perturbations of 2-dimensional degenerate systems. It is proved that if the equilibrium point of the unperturbed system is hyperbolic-type degenerate, then the perturbed sys-tem has a small response solution. The proof is based on the topological degree theory and some KAM techniques developed in [3]. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：500 / 522

页数：23

共 14 条

[1]

[Anonymous], 1996, Lecture Notes in Mathematics

[2] Response solutions to the quasi-periodically forced systems with degenerate equilibrium: a simple proof of a result of W Si and J Si and extensions [J].

Cheng, Hongyu ;

de la Llave, Rafael ;

Wang, Fenfen .

NONLINEARITY, 2021, 34 (01) :372-393

[3] Completely degenerate lower-dimensional invariant tori for Hamiltonian system [J].

Hu, Shengqing ;

Liu, Bin .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 266 (11) :7459-7480

[4] On quasi-periodic perturbations of elliptic equilibrium points [J].

Jorba, A ;

Simo, C .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1996, 27 (06) :1704-1737

[5] ON THE REDUCIBILITY OF LINEAR-DIFFERENTIAL EQUATIONS WITH QUASI-PERIODIC COEFFICIENTS [J].

JORBA, A ;

SIMO, C .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1992, 98 (01) :111-124

[6] CONVERGENT SERIES EXPANSIONS FOR QUASI-PERIODIC MOTIONS [J].

MOSER, J .

MATHEMATISCHE ANNALEN, 1967, 169 (01) :136-&

[7] Response Solutions in Degenerate Oscillators Under Degenerate Perturbations [J].

Si, Wen ;

Yi, Yingfei .

ANNALES HENRI POINCARE, 2022, 23 (01) :333-360

[8] Completely degenerate responsive tori in Hamiltonian systems [J].

Si, Wen ;

Yi, Yingfei .

NONLINEARITY, 2020, 33 (11) :6072-6098

[9] Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems [J].

Si, Wen ;

Si, Jianguo .

NONLINEARITY, 2018, 31 (06) :2361-2418

[10] Construction of response solutions for two classes of quasi-periodically forced four-dimensional nonlinear systems with degenerate equilibrium point under small perturbations [J].

Si, Wen ;

Si, Jianguo .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 262 (09) :4771-4822

← 1 2 →