  We describe an iterative approach to computing long-time semiclassical
dynamics in the presence of chaos, which eliminates the need for summing over
an exponentially large number of classical paths, and has good convergence
properties even beyond the Heisenberg time. Long-time semiclassical properties
can be compared with those of the full quantum system. The method is used to
demonstrate semiclassical dynamical localization in one-dimensional classically
diffusive systems, showing that interference between classical paths is a
sufficient mechanism for limiting long-time phase space exploration.
