On the anisotropic Manev problem

摘要: We consider the Manev potential, given by sum between inverse and square of distance, in an anisotropic space, i.e., such that force acts differently each direction. Using McGehee coordinates, we blow up collision singularity, paste a manifold to phase study flow on near manifold, find positive-measure set orbits. Besides frontal homothetic, nonhomothetic, spiraling collisions ejections, put into evidence surprising class oscillatory ejection infinity further tackle capture escape solutions zero-energy case. By finding connection orbits equilibria and/or cycles at impact infinity, describe large capture-collision ejection-escape solutions.