00-243 Florin Diacu and Manuele Santoprete
Nonintegrability and Chaos in the Anisotropic Manev Problem (45K, LaTeX) May 25, 00
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 00-243.src( 00-243.comments , 00-243.keywords , Manev1.tex )