On the global dynamics of the anisotropic Manev problem

We study the global flow of the anisotropic Manev problem, which describes the planar motion of two bodies under the influence of an anisotropic Newtonian potential with a relativistic correction term. We first find all the heteroclinic orbits between equilibrium solutions. Then we generalize the Poincaré–Melnikov method and use it to prove the existence of infinitely many transversal homoclinic orbits. Invoking a variational principle and the symmetries of the system, we finally detect infinitely many classes of periodic solutions.