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时间可逆系统的等时中心条件 被引量：2

Isochronicity Conditions for Time-Reversible 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横截交换系统的计算.为了减少计算量,对于时间可逆的解析微分系统,给出了系统具有等时中心的两个充要条件,为建立等时中心条件推导的直接方法作理论上的准备. A center is called an isochronous center if those periodic orbits in some neighbourhood have the same period. The main difficulty in proving isochronicity is to find corresponding transversal commuting system. To reduce the computations, this paper gives two necessary and sufficient conditions for isoehronicity of time-reversible systems. These two conditions are theoretically helpful for constructing isochronicity in a direct way.
作者 桑波 伊继金 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 《曲阜师范大学学报（自然科学版）》 CAS 2010年第2期7-9,共3页 Journal of Qufu Normal University(Natural Science)
基金 国家自然科学基金资助项目(10371135)
关键词 时间可逆系统 等时中心 等时性 time-reversible system isochronous center isochronicity
分类号 O175.12 [理学—基础数学]
  • 相关文献

参考文献12

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  • 9桑波,朱思铭.一类可逆三次系统的等时中心[J].系统科学与数学,2008,28(2):129-135. 被引量：4
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二级参考文献13

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共引文献3

同被引文献14

  • 1CHAVARRIGA J,GRAU M.Some open problems related to 16th Hilbert prolem[J].Scientia(Series A:Mathematical Sciences),2003,9(1):1-26.
  • 2CHAVARRIGA J,GARDA I.Isochronous centers of cubic reversible systems[M].Lecture Note in Physics,Dynamical Systems,Plasmas and Gravitation,Springer-Verlag,1999,518:255-268.
  • 3Weinian Z,Xiaorong H,Zhenbing Z.Weak centers and bifurcation of critical periods in reversible cubic systems[J].Computers and Mathematics with Applications,2000,40(6-7):771-782.
  • 4CHEN Xing-wu,ROMANOVSKI V G.Linearizability conditions of time-reversible cubic systems[J].Journal of Mathematical Analysis and Applications,2010,362:438-449.
  • 5SABATINI M.Charactering isochronous centers by Lie brackets[J].Differential Equations Dynam Systems,1997,5(1):91-99.
  • 6Gine J. The nondegenerate center problem and the inverse integrating factor[ J ]. Bull Sci math, 2006,130 : 152-161.
  • 7Chavarriga J, Sabatini M. A survey of isochronous centers[J]. Qual Theory Dyn Syst, 1999,1: 1-70.
  • 8Chavarriga J, Giacomini H, GineJet al. On the integrability of two-dimensional flows [ J ]. J D E, 1999,157:163,182.
  • 9Chavarriga J, Giacomini H, Gine Jet al. Darboux integrability and the reverse integrating factor[ J].J D E ,2003,194:116-139.
  • 10Giacomini H, Llibre J, Viano M. On the nonexistence, existence, and uniqueness of limit cycles [ J ]. Nonlinearity, 1996,9: 501-516.

引证文献2

曲阜师范大学学报（自然科学版）
2010年 第2期

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