We study a two-body problem given by the sum of the Newtonian potential and an anisotropic perturbation that is a homogeneous function of degree -β, β ≥2. For β>2, the sets of initial conditions leading to collisions/ejections and the one leading to escapes/captures have positive measure. For β>2 and β≠3, the flow on the zero-energy manifold is chaotic. For β=2, a case we prove integrable, the infinity manifold of the zero-energy level has heteroclinic connections with the collision manifold.
Diacu, Florin; Pérez-Chavela, Ernesto; and Santoprete, Manuele, "The Kepler Problem with Anisotropic Perturbations" (2005). Mathematics Faculty Publications. 48.