Dynamical evolution of the Correia et al. (2009) resonant fit at various levels of approximation. The black curve corresponds to the solution obtained with numerical N-body integration software (that is by direct integration of the Hamiltonian (1)). The red curves are given by the integrable Hamiltonian (29). The purple curves depict the dynamical evolution derived from the nonintegrable Hamiltonian (48). Following Correia et al. (2009), panel A shows the evolution of resonant argument 3λ₂ − 2λ₁ − ϖ₁. Panel B shows the evolution of the apsidal angle Δγ. Panel C shows the eccentricities as functions of time. The evolution of the second resonant argument, 3λ₂ − 2λ₁ − ϖ₂, can be re-constructed by combining the evolution of 3λ₂ − 2λ₁ − ϖ₁ with that of Δγ.