PERIODIC ORBITS OF THE SPATIAL ANISOTROPIC KEPLER PROBLEM WITH ANISOTROPIC PERTURBATIONS

被引：0
|
作者：
Li, Mengyuan [1 ,2 ]
Liu, Qihuai [3 ,4 ]
机构：
[1] Guilin Univ Elect Technol, Sch Math & Comp Sci, Guilin 541002, Peoples R China
[2] Chengdu Modern Vocat & Tech Sch, Chengdu 610000, Peoples R China
[3] Guilin Univ Elect Technol, Guangxi Coll & Univ Key Lab Data Anal & Computat, Sch Math & Comp Sci, Guilin 541002, Peoples R China
[4] Guangxi Normal Univ, Ctr Appl Math Guangxi, Guilin 541004, Peoples R China
来源：
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年
关键词：
Periodic orbit; averaging theory; residue theorem; spatial anisotropic Kepler problem; 2-BODY PROBLEM; GRAVITATION; PRINCIPLE; STABILITY; SYSTEMS;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we study the periodic orbits of the spatial anisotropic Kepler problem with anisotropic perturbations on each negative energy surface, where the perturbations are homogeneous functions of arbitrary integer degree p. By choosing the different ranges of a parameter beta, we show that there exist at least 6 periodic solutions for p > 1, while there exist at least 2 periodic solutions for p <= 1 on each negative energy surface. The proofs of main results are based on symplectic Delaunay coordinates, residue theorem, and averaging theory.
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页数：42
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