Top: resonant angle, σ, corresponding to stable (continuous lines) and unstable (dashed lines) fixed points for the 1/3 SOR as function of δ. As observed in the 1/2 SOR, both unstable and stable solutions are detected at qσ = 0 for δ ≲ 0. We thus plotted the stable branch at qσ = 0, while the unstable solutions are shown at qσ = 360°. Vertical beige lines identify the mapped values of δ adopted for the phase planes in Fig. 3. System parameters were also preserved from that figure. Bottom: values of σ as function of the eccentricity for the global minimum of F at each value of N (or δ). The conversion from kinematical to dynamical librations occurs at e = e_dyn, while the bifurcation from symmetric to asymmetric librations occurs at e = e_asym.