Variation of the libration frequency versus . The frequency is taken over the purple horizontal line in Fig. 2. Inside the tadpole region, the libration frequency decreases from at L₄ (ζ₀ = 60°) to 0 on the separatrix (ζ₀ = ζ_s ≈ 23.9°). In the horseshoe domain (ζ₀<ζ_s) the frequency increases from 0 on the separatrix to infinity when the two planets get closer because the approximations leading to Eq. (5) are not valid close to the collision (see Robutel & Pousse 2013).