Analytical results for the resonant regions for apsidal resonances centred at σ_1,e = π (left panel) and the associated numerical results for the distribution of the apsidal resonance (right panel). For the numerical results, the initial condition is g₀ = 0 and h₀ = π (corresponding to σ_1,e = π at the initial instant). In the left panel, level curves of the motion integral Σ₂ are presented as background. In the right panel, blue dots stand for resonant trajectories inside islands centred at i = 90°, and red dots show resonant trajectories inside asymmetric islands of libration. The difference arising in the top space is due to the fact that the analytical results are restrained by level curves of the motion integral Σ₂.