Electron. J. Differential Equations, Vol. 2021 (2021), No. 63, pp. 142.
Periodic orbits of the spatial anisotropic Kepler problem with anisotropic perturbations
Mengyuan Li, Qihuai Liu
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.
Submitted April 12, 2020. Published July 8, 2021.
Math Subject Classifications: 37N05, 37G15, 70F05.
Key Words: Periodic orbit; averaging theory; residue theorem; spatial anisotropic Kepler problem.
DOI: https://doi.org/10.58997/ejde.2021.63
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Mengyuan Li
School of Mathematics and Computing Sciences
Guilin University of Electronic Technology
Guilin 541002, China
email: limy9595@163.com


Qihuai Liu
School of Mathematics and Computing Sciences
Guilin University of Electronic Technology
Guilin 541002, China
email: qhuailiu@gmail.com

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