Nonintegrability and chaos in the anisotropic Manev problem

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 periodi c orbits and show that the system is nonintegrable. Finally, using the geod esic deviation approach, we prove the existence of a large nonchaotic set o f uniformly bounded and collisionless solutions, (C) 2001 Elsevier Science B.V. All rights reserved.