Collision dynamics in Hénon-Heiles’ two-body problem

Abstract

We tackle the two-body problem associated to Hénon-Heiles’ potential in the special case of the collision singularity. Using McGehee-type transformations of the second kind, we blow up the singularity and replace it by the collision manifold Mc pasted on the phase spece. We fully describe the flow on Mc. This flow is similar to analogous flows met in post-Newtonian two-body problems.

Keywords

• Celestial mechanics