Dependence of the escape from an axially symmetric galaxy on the energy

The escape of a particle from a dynamical system depends on the intersection between the ingoing and outgoing asymptotic trajectories to certain periodic orbits placed at the openings of the curves of zero velocity of the system. Although many efforts have been devoted to the analysis of the escape from potentials presenting multiple openings, there are still few studies on potentials with only one opening. In this article, we clarify the way in which the energy affects the escape in this type of systems, showing that, contrary to what one could expect, there are several bifurcations for certain values of the energy.