  In recent years, there has been considerable interest in understanding the
motion in Hamiltonian systems when phase space is divided into stochastic and
integrable regions. This paper studies one aspect of this problem, namely, the
motion of trajectories in the stochastic sea when there is a small island
present. The results show that the particle can be stuck close to the island
for very long times. For the standard mapping, where accelerator modes are
possible, it appears that the mean squared displacement of particles in the
stochastic sea may increase faster than linearly with time indicating
non-diffusive behavior.
