On the Global Dynamics of the Anisotropic Manev Problem

Details On the Global Dynamics of the Anisotropic Manev Problem On the Global Dynamics of the Anisotropic Manev Problem

2002-08-07

arxiv.org/abs/nlin/0208012v1

Physica D: Nonlinear Phenomena Volume 194, Issues 1-2, 1 July 2004, Pages 75-94

Nonlinear Sciences

Chaotic Dynamics

29 pages, 4 figures

Scientific paper

10.1016/S0167-2789(01)00248-2

We study the global flow of the anisotropic Manev problem, which describes the planar motion of two bodies under the influence of an anisotropic Newtonian potential with a relativistic correction term. We first find all the heteroclinic orbits between equilibrium solutions. Then we generalize the Poincare'-Melnikov method and use it to prove the existence of infinitely many transversal homoclinic orbits. Invoking a variational principle and the symmetries of the system, we finally detect infinitely many classes of periodic orbits.

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