  The phase space for Hamiltonians of two degrees of freedom is usually divided
into stochastic and integrable components. Even when well into the stochastic
regime, integrable orbits may surround small stable regions or islands. The
effect of these islands on the correlation function for the stochastic
trajectories is examined. Depending on the value of the parameter describing
the rotation number for the elliptic fixed point at the center of the island,
the long-time correlation function may decay as t^-5 or exponentially, but more
commonly it decays much more slowly (roughly as t^-1). As a consequence these
small islands may have a profound effect on the properties of the stochastic
orbits. In particular, there is evidence that the evolution of a distribution
of particles is no longer governed by a diffusion equation.
