## 留言板

Melnikov方法和圆型平面限制性三体问题的横截同宿研究*

 引用本文: 朱如曾, 向程. Melnikov方法和圆型平面限制性三体问题的横截同宿研究*[J]. 应用数学和力学, 1996, 17(12): 1113-1122.
Zhu Ruzeng, Xiang Cheng. Studies of Melnikov Method and Transversal Homoclinic Orbits in the Circular Planar Restricted Three-Body Problem[J]. Applied Mathematics and Mechanics, 1996, 17(12): 1113-1122.
 Citation: Zhu Ruzeng, Xiang Cheng. Studies of Melnikov Method and Transversal Homoclinic Orbits in the Circular Planar Restricted Three-Body Problem[J]. Applied Mathematics and Mechanics, 1996, 17(12): 1113-1122.

## Studies of Melnikov Method and Transversal Homoclinic Orbits in the Circular Planar Restricted Three-Body Problem

• 摘要: 本文对由两自由度近可积哈密顿系统经非正则变换而得到的,具有高阶不动点的非哈密顿系统给出了判别横截同宿轨和横截异宿轨存在性的两条判据。对原二体质量比很小时近可积圆型平面限制性三体问题,采用本文判据证明存在横截同宿轨,从而存在横截同宿穿插现象;还在一定假设下证明了存在横截异宿轨;并给出了全局定性相图。
•  [1] A.Wintner,The Analytical Foundations of Celestial Mechanics,Princeton Univ.Press(1947). [2] T.M.Cherry,On Poincare's theorem of "the non-existence of uniform integrals of dynamical equation",Proc.Cambridge Phil.Soc.,22(1924). [3] V.Szebehely,Long Time Prediction in Dynamics,Ed.by W.Horton and L.Richl,Wiley,Austin(1981). [4] V.Szebehely,Is celestial mechanics deterministicϒ Applications of Modern Dynamics to Celestial Mechanics and Astrodynamics,Ed.by Szebehely,D.Reidel Pub.Company(1982),321-324. [5] R.Easton and R.McGehee,Homoclinic phenomena for orbits doubly asymptotic to an invariant three-sphere,Indiana U.Math.J.,28(1979),211-240. [6] R.Easton,Capture orbits and Melnikov integrals in the planar three-body problem,Cele.Mech.and Dyn.Astro.,50(1991),283-297. [7] R.McGehee,A stable manifold theorem for degenerate fixed points with application to celestial mechanics,J.DiJJ.Eq.,14(1973),70-88. [8] J.Guckenheimer and P.Holmes,Nonlinear Oscillations,Dynamical Systems,and Bifurcations of Vector Fields,Springer-Verlag(1983). [9] S.Wiggins,Global Bifurcations and Chaos,Springer-Verlag(1988).

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##### 出版历程
• 收稿日期:  1995-07-23
• 修回日期:  1996-04-01
• 刊出日期:  1996-12-15

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