Chaotic evolution of a 3:2 resonant system at differing levels of approximation. Panels A) and B) show the orbital eccentricities and the semi-major axis ratio respectively. The initial conditions of the described system correspond to the same level of Ψ₂, as that of the Correia et al. (2009) fit. However, the energy level is chosen such that the motion overlaps the 4:3 resonance. Specifically, the second outermost energy level, plotted in Fig. 5 is considered. As in Fig. 6, the black curve corresponds to the result of a numerical N-body integration. Within the context of the N-body solution, the planets reverse order shortly after the beginning of the integration and subsequently suffer a mutual collision after ~40 years of dynamical evolution. The blue curve represents the results obtained by numerical integration of the perturbative Hamiltonian (32), that contains both resonant arguments. The inadequacy of the integrable approximation (29) (plotted in red) in a chaotic domain can easily be seen.