Periodic Orbits of the Planar Anisotropic Kepler Problem

In this paper, we prove that at every energy level the anisotropic Kepler problem with small anisotropy has two periodic orbits which bifurcate from elliptic orbits of the Kepler problem with high eccentricity. Moreover we provide approximate analytic expressions for these periodic orbits. The tool for proving this result is the averaging theory.

Periodic Orbits of the Anisotropic Kepler Problem with Quasihomogeneous Potentials

In this paper, we analyze the periodic structure of the anisotropic Kepler problem with the same type of perturbations using symplectic Delaunay coordinates and averaging theory. Moreover, sufficient conditions for existence and kind of stability of this class of perturbed Kepler problems are given.