trajectories for different integration times ($T=400,\;1300,\;13000$ days), are depicted by black, red and blue points, respectively in Fig. \[fig:diffesctime\] (a). The longer the integration time the smaller the survival area. Consequently, we can identify a long-lived island as a subset of *shorter time* islands. Nevertheless, a robust filamentary structure encloses the inner compact long-lived island. Refined numerical investigations show that the filamentary structure has a self-similar nature and, therefore, one might expect chaotic behaviour in this part of the phase space.

It is known that in Hamiltonian dynamics the number of non-escaped trajectories shows an exponential decay for shorter times and follows a power-law for longer times ([*see for example Lai & Tél (2011)*]{}). Short time escapes are related to the transversal intersections of the stable and unstable manifolds of the UPOs where the dynamics can be considered fully hyperbolic. Particles with longer life time are confined to that region of phase space where the manifolds intersect tangentially. This phenomenon appears, in fact, close to the border of regular tori and is known as stickiness. The crossover from exponential to power law decay can indeed be seen in Fig. \[fig:diffesctime\] (b).

Fig. \[fig:diffesctime\] (b) shows the two segments. The straight 