Hyperbolicity of elliptic Lagrangian orbits in the planar three body problem

作     者：OU YuWei 

作者机构：Department of MathematicsShandong University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2014年第57卷第7期

页      面：1539-1544页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No.11131004) 

主　　题：planar three-body problem Lagrangian solution hyperbolicity Maslov-type index 

摘      要：The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,9] and the eccentricity e ∈ [0,1）.In this paper we use Maslov-type index to study the stability of these solutions and prove that the elliptic Lagrangian solutions is hyperbolic for β ＆gt; 8 with any eccentricity.