Nonintegrability and Chaos in the Anisotropic Manev Problem

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 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.

References in corpus (2)

• On the Global Dynamics of the Anisotropic Manev Problem
• Nonintegrability and Chaos in the Anisotropic Manev Problem

Cited by in corpus (10)

• The Kepler Problem with Anisotropic Perturbations
• Nonintegrability and Chaos in the Anisotropic Manev Problem
• On the Global Dynamics of the Anisotropic Manev Problem
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• Chaos in Black holes Surrounded by Electromagnetic Fields
• Symmetric Periodic Solutions of the Anisotropic Manev Problem
• On the viability of local criteria for chaos
• Non-Integrability of a weakly integrable Hamiltonian system
• Mel'nikov method revisited
• The Eccentric Frame Decomposition of Central Force Fields