Nilpotent centers of cubic systems

被引：3

作者：

Andreev, A. F. ^{[1
]}

Andreeva, I. A. ^{[2
]}

Detchenya, L. V. ^{[3
]}

Makovetskaya, T. V. ^{[4
]}

Sadovskii, A. P. ^{[4
]}

机构：

[1] St Petersburg State Univ, St Petersburg 199034, Russia

[2] Peter Great Polytech Univ, St Petersburg 195251, Russia

[3] Yanka Kupala State Univ Grodno, Grodno 230023, BELARUS

[4] Belarusian State Univ, Minsk 220030, BELARUS

来源：

DIFFERENTIAL EQUATIONS | 2017年 / 53卷 / 08期

关键词：

CENTER-FOCUS PROBLEM;

D O I：

10.1134/S0012266117080018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present an explicit form of cubic systems with a nilpotent singular point of the focus or center type at the origin. A method for finding the focus quantities of such systems is indicated. Sufficient conditions for the existence of a nilpotent center for cubic systems are given. Cubic systems reducible to the LiA ' enard system are studied in detail.

引用

页码：975 / 980

页数：6

共 50 条

[31] Strongly isochronous centers of cubic systems with degenerate infinity
D. Dolićanin-Đekić
Differential Equations, 2014, 50 : 971 - 975
[32] A class of cubic systems with two centers or two foci
Chen, LS
Lu, ZY
Wang, DM
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 242 (02) : 154 - 163
[33] Global centers of a class of cubic polynomial differential systems
Llibre, Jaume
Rondon, Gabriel
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2024, 73 (05) : 2141 - 2160
[34] THE POINCAR BIFURCATION OF CUBIC HAMILTONIAN SYSTEMS WITH DOUBLE CENTERS
Liu Tiecheng Song Yan (Dept. of Math.
Annals of Applied Mathematics, 2005, (03) : 349 - 352
[35] The Poincare bifurcation of cubic Hamiltonian systems with double centers
Song, Y
Tan, XX
DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, 2006, 13 : 1046 - 1053
[36] Nondegenerate centers and limit cycles of cubic Kolmogorov systems
Antonio Algaba
Cristóbal García
Jaume Giné
Nonlinear Dynamics, 2018, 91 : 487 - 496
[37] Analytically Integrable Centers of Perturbations of Cubic Homogeneous Systems
Algaba, Antonio
Garcia, Cristobal
Reyes, Manuel
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2021, 20 (02)
[38] Bifurcation for a class of piecewise cubic systems with two centers
Ji, Guilin
Sun, Yangjian
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2022, (46) : 1 - 12
[39] Strongly isochronous centers of cubic systems with degenerate infinity
Dolicanin-Dekic, D.
DIFFERENTIAL EQUATIONS, 2014, 50 (07) : 971 - 975
[40] The cyclicity of period annuli for a class of cubic Hamiltonian systems with nilpotent singular points
Yang, Jihua
Zhao, Liqin
JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (09) : 5554 - 5581

← 1 2 3 4 5 →