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 50 条

[1] Response Solutions of Degenerate Quasi-Periodic Systems Under Small Perturbations
Song Ni
Junxiang Xu
[J]. Qualitative Theory of Dynamical Systems, 2023, 22
[2] Response solutions of 2-dimensional degenerate systems under quasi-periodic perturbations
Ma, Zhichao
Qu, Ru
Xu, Junxiang
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 360 : 500 - 522
[3] Response Solutions for Completely Degenerate Oscillators Under Arbitrary Quasi-Periodic Perturbations
Zhichao Ma
Junxiang Xu
[J]. Communications in Mathematical Physics, 2023, 402 : 1 - 33
[4] Response Solutions for Completely Degenerate Oscillators Under Arbitrary Quasi-Periodic Perturbations
Ma, Zhichao
Xu, Junxiang
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2023, 402 (01) : 1 - 33
[5] RESPONSE SOLUTIONS OF A CLASS OF DEGENERATE QUASI-PERIODIC SYSTEMS WITH A SMALL PARAMETER
Yang, Xiaomei
Xu, Junxiang
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2024, 44 (02) : 537 - 551
[6] Response solutions of 3-dimensional degenerate quasi-periodic systems with small parameter
Xu, Junxiang
Li, Qi
Wang, Jun
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 293 : 188 - 225
[7] Degenerate Resonances and Synchronization in Nearly Hamiltonian Systems Under Quasi-periodic Perturbations
Morozov, Albert D.
Morozov, Kirill E.
[J]. REGULAR & CHAOTIC DYNAMICS, 2022, 27 (05): : 572 - 585
[8] Degenerate Resonances and Synchronization in Nearly Hamiltonian Systems Under Quasi-periodic Perturbations
Albert D. Morozov
Kirill E. Morozov
[J]. Regular and Chaotic Dynamics, 2022, 27 : 572 - 585
[9] QUASI-PERIODIC SOLUTIONS FOR THE TWO-DIMENSIONAL SYSTEMS WITH AN ELLIPTIC-TYPE DEGENERATE EQUILIBRIUM POINT UNDER SMALL PERTURBATIONS
Jiao, Jinjing
Shi, Guanghua
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2020, 19 (11) : 5157 - 5180
[10] Quasi-Periodic Solutions for Differential Equations with an Elliptic-Type Degenerate Equilibrium Point Under Small Perturbations
Li, Xuemei
Shang, Zaijiu
[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2019, 31 (02) : 653 - 681

← 1 2 3 4 5 →