Non-Hyperbolic Equilibria in the Charged Collinear Three-Body Problem

Consider three charged masses moving along the line. For this model we study the solutions near total collision using blow up techniques obtaining that for given masses and charges the vector field on the collision manifold has a non-hyperbolic equilibrium point. To study this situation the vector field is written in normal form and the center manifold theory is used obtaining that all nonzero solutions near the origin escape to infinity.