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