On the anisotropic Manev problem

We consider the Manev potential, given by the sum between the inverse and t he inverse square of the distance, in an anisotropic space, i.e., such that the force acts differently in each direction. Using McGehee coordinates, w e blow up the collision singularity, paste a collision manifold to the phas e space, study the flow on and near the collision manifold, and find a posi tive-measure set of collision orbits. Besides frontal homothetic, frontal n onhomothetic, and spiraling collisions and ejections, we put into the evide nce the surprising class of oscillatory collision and ejection orbits. Usin g the infinity manifold, we further tackle capture and escape solutions in the zero-energy case. By finding the connection orbits between equilibria a nd/or cycles at impact and at infinity, we describe a large class of captur e-collision and ejection-escape solutions. (C) 1999 American Institute of P hysics. [S0022-2488(99)01903-9].