Variational property of periodic Kepler orbits in constant curvature spaces

被引：3

作者：

Deng, Yanxia ^{[1
]}

Diacu, Florin ^{[2
]}

Zhu, Shuqiang ^{[3
]}

机构：

[1] Univ Victoria, Victoria, BC, Canada

[2] Natl Univ Singapore, Yale NUS Coll, Singapore, Singapore

[3] Univ Sci & Technol China, Sch Math Sci, Hefei, Anhui, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2019年 / 267卷 / 10期

关键词：

Curved N-body problem; Kepler problem; Closed orbits; Maslov-type index; Morse index; Variational method; MASLOV-TYPE INDEX; 3-BODY PROBLEM; RELATIVE EQUILIBRIA; STABILITY; POINTS; SPHERE;

D O I：

10.1016/j.jde.2019.06.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the variational property of the periodic Kepler orbits on the sphere, the plane and the hyperbolic plane. We first classify the orbits by the two constants of motion: the energy and the angular momentum. Then, we characterize the local variational property of the closed orbits by computing the Maslov-type indices. Finally, we study the global variational property of the closed orbits. We prove that the closed orbits on the hyperbolic plane minimizes the action among all loops which encircle the attracting center. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：5851 / 5869

页数：19

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