- 00-243 Florin Diacu and Manuele Santoprete
- Nonintegrability and Chaos in the Anisotropic Manev Problem
May 25, 00
(auto. generated ps),
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Abstract. 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
Poincar\'e-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.