Maps for distributions and their time evolution

Many dynamical stochastic processes occur "on top" of a deterministic proce ss. We present a method which uses the trajectory of the deterministic proc ess as basis functions for quasiarbitrary distributions. A map for the stoc hastic process can then be computed. This may have applications in electron storage rings or other devices perturbed by a small stochasticity. In this paper we will look only at the most elementary applications of the method. [S1063-651X(99)05310-6].