by the unstable manifold of the chaotic saddle (Slíz, Süli & Kovács 2015) which encloses the regular islands surrounding the stable periodic orbit. This domain of the phase space, where the saddle and the remnants of the outermost KAM torus form a “fat” fractal set, is responsible for the stickiness effect, one of the fundamental phenomena in Hamiltonian escape dynamics with mixed phase space (Contopoulos & Harsoula 2008; Tél & Lai 2008).

We started test particles close to the triangular libration point $L_5$ of the restricted three body problem (RTBP) and analyzed their short and long time dynamics in the presence of a third large body (the Sun), (RFBP).

As it has already been shown (Érdi et al. 2007; Freistetter 2006; Schwarz et al. 2009), the size and the position of the regular domain around the triangular points depend on several parameters such as the mass, eccentricity and the orbital position.

Starting a test particle from the vicinity of the $L_4$, $L_5$ points in the RFBP is not a guarantee that this trajectory will be stable for a long time or that the particle will remain in the system. This is a consequence deriving from the general fact in Hamiltonian 