Techniques based on ergodic theory can be used to help understand the mixing and transport processes in dynamical systems. The main tool is the transfer operator, which describes the action of an autonomous dynamical system on a entire distribution of initial points, rather than on the points individually.

The eigenfunctions of this operator have been used to identify "almost invariant" partitions of the phase space into regions that interact only weakly. For many applications such as fluid motion, we want to understand non-autonomous systems, where the dynamics is time-dependent. Using some new Multiplicative Ergodic Theorems, it's shown show how the transfer operator methods can be generalised to this setting to allow the identification of partitions into weakly interacting time-dependent "coherent sets".