Periodic orbits of the planar anisotropic Manev problem and of the perturbed hydrogen atom problem

Abstract

In this paper we use the averaging theory for studying the periodic solutions of the planar anisotropic Manev problem and of two perturbations of the hydrogen atom problem. When a convenient parameter is sufficiently small we prove that for every value e∈ (0, 1) a unique elliptic periodic solution with eccentricity e of the Kepler problem can be continued to the mentioned three problems.