On the families of periodic orbits of the Sitnikov problem

被引：36
|
作者：
Llibre, Jaume [1 ]
Ortega, Rafael [2 ]
机构：
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain
[2] Univ Granada, Fac Ciencias, Dept Matemat Aplicada, E-18071 Granada, Spain
来源：
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2008年 / 7卷 / 02期
关键词：
3-body problem; Sitnikov problem; periodic orbits; global continuation;
D O I：
10.1137/070695253
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The main goal of this paper is to study analytically the families of symmetric periodic orbits of the elliptic Sitnikov problem for all values of the eccentricity in the interval [0, 1), providing qualitative and quantitative information on the bifurcation diagram of such families of periodic orbits. The basic tool for proving our results is the global continuation method of the zeros of a function depending on one parameter provided by Leray and Schauder and based in the Brouwer degree.
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页码：561 / 576
页数：16
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