  The anisotropic Manev problem, which lies at the intersection of classical,
quantum, and relativity physics, describes the motion of two point masses in an
anisotropic space under the influence of a Newtonian force-law with a
relativistic correction term. Using an extension of the Poincare'-Melnikov
method, we first prove that for weak anisotropy, chaos shows up on the
zero-energy manifold. Then we put into the evidence a class of isolated
periodic orbits and show that the system is nonintegrable. Finally, using the
geodesic deviation approach, we prove the existence of a large non-chaotic set
of uniformly bounded and collisionless solutions.
