Examples of the evolution of the quantities e₂ and Δϖ for different initial conditions. The black dashed lines represent the direction of the anti-Lagrangian configuration while the black solid line is the direction of the Eccentric Lagragian equilibria. In both cases, the initial conditions are ω₂ = ω₁ + π, I₁ = I₂ = 0, m₁ = 10m₂ = 1 × 10⁻⁴m₀, a₁ = a2 = 1 au, e₁ = 0.1, e₂ = m₁e₁/m₂ and ζ = 60°. Each trajectory is integrated for 20 Kyr, with the initial conditions represented by the black triangle, and the colour code representing the time (blue at t = 0, yellow at 20 Kyr). On the left panel, τ_e2/τ_a1 = 5, while on the rightτ_e2/τ_a1 = 20. In both cases, τ_a1/τ_a2 = 0.01.