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一类时间可逆四次系统的等时中心 被引量：1

Isochronicity Conditions for Time-Reversible Quartic Systems
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摘要 当中心邻域的闭轨周期为常数时,该中心称为等时中心.解决等时中心问题的主要难点在于周期系数代数簇的分解和横截交换系统的计算.对于一类含有三次非线性项的时间可逆四次系统,给出了周期系数的递推算法,在此基础上,利用吴方法得到了系统具有等时中心的充要条件. A center is called an isochronous center if those periodic orbits in some neighbourhood of it have the same period.The main difficulty in proving isochronicity is algebraic variety decompositions for period coefficients and finding transversal commuting systems.For a class of time-reversible quartic system with third order terms,a recursive algorithm for computing period coefficients is given,with which necessary and sufficient conditions for isochronicity are obtained by Wu Wen-tsun method.
作者 桑波 刘文健 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 《西南师范大学学报（自然科学版）》 CAS CSCD 北大核心 2011年第4期59-63,共5页 Journal of Southwest China Normal University(Natural Science Edition)
基金 国家自然科学基金资助项目(10371135)
关键词 时间可逆系统 四次系统 等时中心 等时性 time-reversible systems quartic system isochronous center isochronicity
分类号 O175.12 [理学—基础数学]
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参考文献10

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同被引文献11

  • 1王铎,毛锐.计算Lyapunov量的复算法[J].自然科学进展（国家重点实验室通讯）,1995,5(6):754-757. 被引量：6
  • 2刘一戎,李继彬.论复自治微分系统的奇点量[J].中国科学（A辑）,1989,20(3):245-255. 被引量：94
  • 3WANG Dong-ming. Mechanical Manipulation for a Class of Differential Systems [J]. Journal of Symbolic Computation, 1991, 12(2): 233-254.
  • 4WANG Duo. A Recursive Formula and Its Application To Computations of Normal Forms and Focal Values [C]//LIAO Shawtao, YE Yan-qian. Dynamical Systems. Singapore: World Sci Publ, 1993:238 -247.
  • 5YU Pei. Computation of Normal Forms Via a Perturbation Technique [J]. Journal of Sound and Vib, 1998, 211(1): 19-38.
  • 6ALGABA A, FREIRE E, GAMERO E. Isochronicity via Normal Form[J]. Qual Theory Dyn Syst, 2000, 1 (2): 133-156.
  • 7GARCIA I A, GRAU M. A Survey on the Inverse Integrating Factor [J]. Qual Theory Dyn Syst, 2010, 9 (1-2): 115-166.
  • 8LLOYD N G, PEARSON J M. Symmetry in Planar Dynamical Systems [J]. Journal of Symbolic Computation, 2002, 33(3): 357-366.
  • 9JIN Xiao-fan, WANG Dong-ming. On the Conditions of Kukles for the Existence of a Centre [J].Bulletin of London Mathematical Society, 1990, 22(1): 1-4.
  • 10TEIXEIRA M A, YANG Jia zhong. The Center-Foucs Problem and Reversibility [J]. Journal of Differential Equations, 2001, 174(1): 237-251.

引证文献1

西南师范大学学报（自然科学版）
2011年 第4期

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