Symmetric periodic solutions of the anisotropic Manev problem

Abstract

We consider the Manev potential in an anisotropic space, i.e., such that the force acts differently in each direction. Using a generalization of the Poincaré continuation method we study the existence of periodic solutions for weak anisotropy. In particular we find that the symmetric periodic orbits of the Manev system are perturbed to periodic orbits in the anisotropic problem.