ar X iv : a da p - or g / 97 08 00 5 v 1 1 1 A ug 1 99 7 Dynamics controlled by additive noise

Analysis is presented of a system whose dynamics are dramatically simplified by tiny amounts of additive noise. The dynamics divide naturally into two phases. In the slower phase, trajectories are close to an invariant manifold; this allows small random disturbances to exert a controlling influence. A map is derived which provides an accurate description of the trajectories.