On the Manev spatial isosceles three-body problem

Abstract

We study the isosceles three-body problem with Manev interaction. Using a McGehee-type technique, we blow up the triple collision singularity into an invariant manifold, called the collision manifold, pasted into the phase space for all energy levels. We find that orbits tending to/ejecting from total collision are present for a large set of angular momenta. We also find that as the angular momentum is increased, the collision manifold changes its topology. We discuss the flow near-by the collision manifold, study equilibria and homographic motions, and prove some statements on the global flow.