Structure of the phase plane (k, h) = (e cos 2σ, e sin 2σ) for the 1/3 SOR for a Quaoar-like central body. All plots were constructed assuming a mass anomaly with $\overline{\mu }$ = m₁/m_c = 10⁻². Different values of δ allow us to visualize the transition from symmetric near-resonant motion (top left) to asymmetric libration of increasing eccentricity. The separatrices are highlighted with dashed lines. Contrary to the 1/2 SOR, the low-eccentricity dynamical librations are symmetric, while the asymmetric domain only appears for e ≳ 0.07. Note the change in the eccentricity limits in the different frames.