Almost-invariant sets as ``ghost rods'' for fluid stirring

In two-dimensional time-dependent flows or three-dimensional flows with a certain symmetry, the braiding of periodic orbits provides a framework for analyzing chaos in the system through application of the Thurston-Nielsen (TN) classification theorem. ``Ghost rods,'' or periodic orbits generated by the dynamics, behave as physical obstructions that ``stir'' the surrounding fluid, and these can be used as the basis for this topological analysis. We explore the identification of almost-invariant sets, or regions of fluid with high local residence time, as ghost rods. This set-oriented approach can be applied using relatively coarse system information, making this a promising approach for extending the use of the TN classification theorem to a variety of fluid systems.