Structure of the phase plane for the 1/2 SOR for a Quaoar-like central body. All plots were constructed assuming a mass anomaly with $\overline{\mu }$ = m₁/m_c = 10⁻² and transformed to regular variables (k, h) = (e cos σ, e sin σ). Different values of δ allow us to visualize the transition from symmetric near-resonant motion (top left) to asymmetric libration of increasing eccentricity (bottom right). A second separatrix and an inner circulation region appear at δ ≲ −0.01. Note the change in the eccentricity limits in the lower-right panel.