Return Time Dynamics as a Tool for Finding Almost Invariant Sets

TL;DRAbstract

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 Poincaré section in the planar circular restricted three body problem into various sets.

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