Solution of center-focus problem for a class of cubic systems

被引：0
作者：
Bo Sang
Chuanze Niu
机构：
[1] Liaocheng University,School of Mathematical Sciences
来源：
Chinese Annals of Mathematics, Series B | 2016年 / 37卷
关键词：
Center variety; Isochronous center; Center conditions; Integrating factor; 34C05; 34C07;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
For a class of cubic systems, the authors give a representation of the nth order Liapunov constant through a chain of pseudo-divisions. As an application, the center problem and the isochronous center problem of a particular system are considered. They show that the system has a center at the origin if and only if the first seven Liapunov constants vanish, and cannot have an isochronous center at the origin.
引用
收藏
页码：149 / 160
页数：11
相关论文
共 21 条
  • [1] Solution of Center-Focus Problem for a Class of Cubic Systems
    Bo SANG
    Chuanze NIU
    Chinese Annals of Mathematics(Series B), 2016, 37 (01) : 149 - 160
  • [2] Solution of Center-Focus Problem for a Class of Cubic Systems
    Sang, Bo
    Niu, Chuanze
    CHINESE ANNALS OF MATHEMATICS SERIES B, 2016, 37 (01) : 149 - 160
  • [3] The center-focus problem of a class of polynomial differential systems with degenerate critical points
    Huang, Wentao
    Liu, Yirong
    Zhu, Fanglai
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2009, 10 (09) : 1167 - 1179
  • [4] THE CENTER-FOCUS PROBLEM AND BIFURCATION OF LIMIT CYCLES IN A CLASS OF 7TH-DEGREE POLYNOMIAL SYSTEMS
    Sang, Bo
    Wang, Qinlong
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2016, 6 (03): : 817 - 826
  • [5] Center problem and bifurcation behavior for a class of quasi analytic systems
    Du, Chaoxiong
    Chen, Haibo
    Liu, Yirong
    APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (09) : 4665 - 4675
  • [6] Nine Limit Cycles Around a Weak Focus in a Class of Three-Dimensional Cubic Kukles Systems
    Yuting Ouyang
    Dongping He
    Wentao Huang
    Qualitative Theory of Dynamical Systems, 2024, 23
  • [7] Nine Limit Cycles Around a Weak Focus in a Class of Three-Dimensional Cubic Kukles Systems
    Ouyang, Yuting
    He, Dongping
    Huang, Wentao
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2024, 23 (03)
  • [8] COMPUTING CENTER CONDITIONS FOR CERTAIN CUBIC SYSTEMS
    LLOYD, NG
    PEARSON, JM
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1992, 40 (03) : 323 - 336
  • [9] Bifurcation of Limit Cycles and Isochronous Centers on Center Manifolds for a Class of Cubic Kolmogorov Systems in R3
    Gu, Jieping
    Zegeling, Andre
    Huang, Wentao
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2023, 22 (02)
  • [10] Center Conditions for A Class of Poincare Systems
    Xu, Jinya
    Lu, Zhengyi
    PROCEEDINGS OF THE 7TH CONFERENCE ON BIOLOGICAL DYNAMIC SYSTEM AND STABILITY OF DIFFERENTIAL EQUATION, VOLS I AND II, 2010, : 766 - 772
123