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Solution of Center-Focus Problem for a Class of Cubic Systems

Solution of Center-Focus Problem for a Class of Cubic Systems
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摘要 For a class of cubic systems, the authors give a representation of the n th 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.
作者 Bo SANG Chuanze NIU
机构地区 School of Mathematical Sciences
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2016年第1期149-160,共12页 数学年刊（B辑英文版）
基金 supported by the National Natural Science Foundation of China(No.11401285) the Foundation for Research in Experimental Techniques of Liaocheng University(No.LDSY2014110)
关键词 Center variety Isochronous center Center conditions Integrating factor 三次系统 焦点问题 Liapunov 求解 中心问题 李雅普诺夫 常数 等时
分类号 O175 [理学—基础数学]
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参考文献20

  • 1Poincar, H., Mmoire sur les courbes d4finies par les 4quations diffrentieUes, J. Math. Pures Appl., 1, 1885, 167-244.
  • 2Malkin K. E., Criteria for the center for a certain differential equation, Volz. Mat. Sb. Vyp., 2, 1964, 87-91.
  • 3Chavarriga J. and Gin6 J., Integrability of cubic systems with degenerate infinity, Differ. Equas Dynam. Syst., 6, 1998, 425-438.
  • 4Sadovskii A. P. and Shcheglova T. V., Solution of center-focus problem for a nine-parameter cubic system, Differ. Equas., 47, 2011, 208-223.
  • 5Hill J. M., Lloyd N. G. and Pearson J. M., Algorithmic derivation of isochronicity conditions, Nonlin. Anal.: Theory, Methods and Applications, 67, 2007, 52-69.
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  • 8Chen X. W. and Romanovski V. G., Linearizability conditions of time-reversible cubic systems, J. Math. Anal. Appl., 362, 2010, 438-449.
  • 9Zhang W. N., Hou X. R. and Zeng Z. B., Weak centers and bifurcation of critical periods in reversible cubic system, Comput. Math. Appl., 40, 2000, 771-782.
  • 10Chavarriga J. and Sabatini M., A survey of isochronous centers, Qualitative Theory of Dynamical Systems, 1, 1999, 1-70.
Chinese Annals of Mathematics,Series B
2016年 第1期

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