Equilibrium curves showing the loci of the stable resonant equilibrium points calculated as explained in the text, in the case of a 3:2 – 3:2 mean motion resonance chain, with m₁ = m₂ = m₃ = 10⁻⁴M_*. The full curves are calculated using the expanded Keplerian Hamiltonian (Eq. (11)), while the dashed curves are calculated using the unexpanded Keplerian Hamiltonian (Eq. (6)), showing very little difference down to very small eccentricities and for reasonable values of the nearly exactly resonant semi-major axis ratio. The location of the nominal resonant semi-major axis ratio (3/2)^2/3 is shown bya vertical orange line. We also superimpose the numerically computed evolution of a three-planet system deep in the 3:2 mean motion resonance (for both pairs) and undergoing dissipative evolution depicted with transparent lines: the system follows the locations of the equilibrium points, which are close to the curves calculated analytically.