  The dissolution process of star clusters is rather intricate for theory. We
investigate it in the context of chaotic dynamics. We use the simple Plummer
model for the gravitational field of a star cluster and treat the tidal field
of the Galaxy within the tidal approximation. That is, a linear approximation
of tidal forces from the Galaxy based on epicyclic theory in a rotating
reference frame. The Poincar\'e surfaces of section reveal the effect of a
Coriolis asymmetry. The system is non-hyperbolic which has important
consequences for the dynamics. We calculated the basins of escape with respect
to the Lagrangian points $L_1$ and $L_2$. The longest escape times have been
measured for initial conditions in the vicinity of the fractal basin
boundaries. Furthermore, we computed the chaotic saddle for the system and its
stable and unstable manifolds. The chaotic saddle is a fractal structure in
phase space which has the form of a Cantor set and introduces chaos into the
system.
