This topic is concerned with the application of computational
dynamics tools to the problem of transport in celestial mechanics and
molecular systems. The celestial problems are typified by computing the
probability that a member of the Hilda group of asteroids (which are
just inside the orbit of Jupiter) cross the orbit of Mars in a certain
interval of time. In the molecular context, the computation of the
ionization rate of the Rydberg atom will be used to illustrate the
techniques.