Critical eccentricities for the 1/3 SOR, associated with changes in the resonant domain, as function of the rotational period of the central body. Different colored curves correspond to different values for the mass anomaly $\overline{\mu }$ = m₁/m_c. The rotational periods for the minor bodies with rings and/or disks are highlighted with vertical beige lines. The values of e_dyn mark the first appearance of dynamical librations, while e_asym signal the bifurcation of symmetric librations (at qσ = π) and the appearance of asymmetric solutions.