Section 5 presents some numerical results for the regions of initial conditions which will results in a given number of bounces against the wall in the canonical variables, analogous to those of section 3 for the original variables. The next two sections of the work analyse these numerical results in some detail, focussing on the behaviour of the mapping on two planes which comprise boundaries of the region of interest. The paper concludes by proposing a number of further questions related to the problem.