Level plots of the Hamiltonian on the (ecosσ,esinσ) plane for different values of N and p. This is the case of k′ = 4, k = 1, with e′ = 0.1, a′ = 1 AU, and μ = 10^-3 for the perturber (in units where ). The black dot in each panel indicates the position of the stable equilibrium point that is found by our algorithm. The function is periodic in σ with period 2π/ (k′ − k), so there will always be k′ − k equivalent stable equilibra one rotation away from each another. We note that e_eq increases with N, while p has the effect of simply rotating the diagram.