Long-term dynamics of Titan as it migrates away from Saturn. Saturn is assumed to remain locked in secular spin–orbit resonance with s₈ at all time; we take its obliquity evolution at the centre of the resonance (red curve in Fig. 18). Titan evolves according to the secular Hamiltonian function given in Eq. (1) in which its semi-major axis is a slowly varying parameter. The top and bottom panels give two outcomes of the chaotic transitions obtained by using a slightly different migration rate. In all panels, the blue curve shows the location of the circular Laplace state P₁, and the red curve shows the location of the eccentric Laplace state P.