Periodic orbits of the spatial anisotropic Kepler problem with anisotropic perturbations

Date

2021-07-08

Authors

Li, Mengyuan
Liu, Qihuai

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

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 β, 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.

Description

Keywords

Periodic orbit, Averaging theory, Residue theorem, Spatial anisotropic Kepler problem

Citation

Li, M., & Liu, Q. (2021). Periodic orbits of the spatial anisotropic Kepler problem with anisotropic perturbations. <i>Electronic Journal of Differential Equations, 2021</i>(63), pp. 1-42.

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Attribution 4.0 International

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