Diffusion index ζ_ν as a function of δ and ξ₀. The planetary masses are as in Table 1 and the chain is 1:1:2. The top of the figure, at ξ₀ ≈ 60°, is the main branch. The blue-to-green regions are almost quasi-periodic (stable), while the red regions are chaotic (unstable). The secular resonances between the libration frequency ν and the precession frequency of the pericentres ν₃, predicted by the analytical results (see Fig. 1), are visible, especially the resonance 1 : 1, which can lead to chaotic orbits for high enough values of the libration amplitude. The horseshoe-shaped orbits at the bottom are mostly chaotic, as expected, since m₁ + m₂ = 2 × 10⁻⁴ is close to the limit 3 × 10⁻⁴ of their existence (Leleu et al. 2015). The main branch around the 1:1 resonance between ν and ν₃ is tidally attractive (see Fig. 7). Systems undergoing tides entering this zone can either converge towards the top of the figure or can become completely chaotic.