A random dynamical system (RDS) is a combination of a measurable dynamical system and a continuous non-autonomous dynamical system, linked with the basic system in skew product form. Time may be discrete or continuous. The concept of RDS unifies several situations incorporating random influences. These range from the throwing of dice over random perturbations of deterministic dynamical systems, for instance by numerical approximations, to stochastic differential equations.

The influence of the randomness in question on the asymptotic behaviour of a perturbed deterministic system is of interest. Concepts are introduced in order to make this more precise and which allow to find some answers, while also qualitatively new phenomena appear. One of these concepts are random attractors. These are discussed in some more detail.