Abstract
In this paper we study the two-body problem that describes the motion of two-point masses in an anisotropic space under the influence of a Newtonian force-law with two relativistic correction terms. We will show that the set of initial conditions leading to collisions and ejections have positive measure and study the capture and escape solutions in the zero-energy case using the infinity manifold. We will also apply the Melnikov method to show that the flow on the zero-energy manifold of another potential which is the sum of the classical Keplerian potential and two anisotropic perturbation which also take into account two relativistic correction terms is chaotic.
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