Return time dynamics as a tool for finding almost invariant sets

The primary goal of transport theory is to compute the rate at which parts of the phase space of a given dynamical system move from one region to another. In this paper we present a new approach for the identification of those regions in phase space that are relevant for transport computations. More concretely, we construct a decomposition into almost invariant sets-that is, those sets that represent the main sources and sinks for transport phenomena-using return time dynamics. We illustrate this technique by partitioning a certain Poincare section in the planar circular restricted three body problem into various sets.