On the anisotropic Manev problem

Date

2010-05-31T15:47:42Z

Authors

Craig, Scott
Diacu, Florin
Lacomba, Ernesto A.
Perez, Ernesto

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Abstract

The anisotropic Manev problem describes the motion of two bodies in an Euclidean space in which the gravitational force acts differently in each direction. The potential is the sum between the inverse and the inverse square of the distance, where the distance is defined such that it embodies the anisotropy of the space. Using McGehee coordinates, we blow up the collision singularity, paste a collision manifold to the phase space, study the flow on and near the collision manifold, and find a rich set of collision orbits having positive measure. In the zero-energy case we describe all possible connections between equilibria and/or cycles at collision and at infinity and find the main qualitative features of the flow.

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