Periodic orbits of the spatial anisotropic Kepler problem with anisotropic perturbations
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Date
2021-07-08
Authors
Li, Mengyuan
Liu, Qihuai
Journal Title
Journal ISSN
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. Electronic Journal of Differential Equations, 2021(63), pp. 1-42.
Rights
Attribution 4.0 International