Li, MengyuanLiu, Qihuai2021-08-272021-08-272021-07-08Li, 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. 1-42.1072-6691https://hdl.handle.net/10877/14473In 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.Text42 pages1 file (.pdf)enAttribution 4.0 InternationalPeriodic orbitAveraging theoryResidue theoremSpatial anisotropic Kepler problemArticle