Variational property of periodic Kepler orbits in constant curvature spaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Deng, Yanxia¹  Diacu, Florin²  Zhu, Shuqiang³ 

[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

关键词: Curved N-body problem;    Kepler problem;    Closed orbits;    Maslov-type index;    Morse index;    Variational method;   

DOI  :  10.1016/j.jde.2019.06.008

来源: Elsevier

【 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.

【 授权许可】

Free