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一类可逆三次系统的等时中心 被引量：4

ISOCHRONOUS CENTER OF A CUBIC REVERSIBLE SYSTEM
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摘要 对于一般多项式系统,给出可逆代数条件推导算法;对于一类可逆三次系统,提出周期系数改进算法,得到原点为等时中心的充要条件. t For polynomial systems, an algorithm to deduce time-reversible conditions is given; For a cubic reversible system, an improved algorithm for computing period coefficients are introduced, and the necessary and sufficient conditions for the orgin to be isochronous center are obtained.
作者 桑波 朱思铭
机构地区 聊城大学数学科学学院 中山大学数学与计算科学学院
出处 《系统科学与数学》 CSCD 北大核心 2008年第2期129-135,共7页 Journal of Systems Science and Mathematical Sciences
基金 国家自然科学基金(10371135)资助项目
关键词 三次系统 可逆系统 周期系数 等时中心 Cubic system, reversible system, period coefficient, isochronous center.
分类号 O175.1 [理学—基础数学]
  • 相关文献

参考文献12

  • 1Loud W. Behavior of the period of solutions of certain plane autonomous systems near centers. Contribution to Differential Equations, 1964, 3(1): 21-36.
  • 2Pleshkan I. A new method of investigating the isochronicity of a system of two differential equations. Diff. Equa., 1969, 5(4): 796-802.
  • 3Christopher C and Devlin J. Isochronous centres in planar polynomial systems. SIAM J. Math. Anal., 1997, 28(1): 162-177.
  • 4Chavarriga J, Gine J and Garcfa I. Isochronous centers of cubic systems with degenerate infinity. Differential Equations and Dynamical Systems, 1999, 7(1): 49-66.
  • 5Mardesic P, Rousseau C, Toni B. Linearization of isochronous centers. J. Diff. Equa., 1995, 121(1): 67-108.
  • 6Chavarriga J and Garcia I. Isochronous centers of cubic reversible systems. Lecture Notes in Physics, Dynamical Systems, Plasmas and Gravitation, Spring-Verlag, 1999, 518: 255-268.
  • 7Weinian Z, Xiaorong H and Zhenbing Z. Weak centers and bifurcation of critical periods in reversible cubic systems. Computers and Mathematics with Applications, 2000, 40(6--7): 771-782.
  • 8Chavarriga J and Grau M. Some open problems related to 16th Hilbert problem. Scientia (Series A: Mathematical Sciences), 2003, 9(1): 1-26.
  • 9Lloyd N and Pearson J. Symmetry in planar systems. J. Symb. Comp., 2002, 33(3): 357-366.
  • 10王东明.消元法及其应用.科学出版社,2002,30-43.

同被引文献36

  • 1谢向东,陈凤德.一类三次系统的极限环个数与奇点分支[J].系统科学与数学,2005,25(4):414-422. 被引量：15
  • 2谢向东,陈凤德.一类具有二虚不变直线的三次系统的极限环与分支[J].数学物理学报（A辑）,2005,25(4):538-545. 被引量：9
  • 3杨宇俊,张剑峰.一类三次系统的极限环与分支问题[J].高校应用数学学报（A辑）,2006,21(4):405-412. 被引量：11
  • 4Loud W.Behavior of the period of solutions of certain plane autonomous systems near centers[J].Contribution to Differential Equations,1964,3(1):21-36.
  • 5Pleshkan I.A new method of investigating the isochronicity of a system of two differential equations[J].Diff Equa,1969,5(4):796-802.
  • 6Christopher C,Devlin J.Isochronous centers in planar polynomial systems[J].SIAM J Math Anal,1997,28(1):162-177.
  • 7Chavarriga J,Giné J,García I.Isochronous centers of cubic systems with degenerate infinity[J].Differential Equations and Dynamical Systems,1997,7(1):49-66.
  • 8Chavarriga J,Grau M.Some open problems related to 16th Hilbert problem[J].Scientia(Series A:Mathematical Sciences),2003,9(1):1-26.
  • 9Chavarriga J,Sabatini M.A survey of isochronous centers[J].Qualitative theory of Dynamical Systems,1999,(1):1-70.
  • 10Chavarriga J,García I.Isochronous centers of cubic reversible systems[M].Lecture Note in Physics,Dynamical Systems,Plasmas and Gravitation,Springer-Verlag,1999,518:255-268.

引证文献4

二级引证文献4

系统科学与数学
2008年 第2期

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