Orbital evolution with time for two TNOs near the Kozai resonance over 100 Myr for initial I = 30°. We show the semi-major axis, the eccentricity, the inclination, the resonant angle σ₀, and the argument of the pericentre (from top to bottom). The initial conditions correspond to the black dots in Fig. 11; i.e. a = 63.1 au, e = 0.5, and σ₀ = 200° (top), and a = 63.1 au, e = 0.7, and σ₀ = 300° (bottom).