Mixing and coherence are fundamental issues
at the heart of understanding fluid dynamics and other non-autonomous dynamical
systems. Recently the notion of coherence has come to a more rigorous footing,
in particular, within the studies of finite-time nonautonomous dynamical systems.
Here we recall “shape coherent sets” which is proven to correspond to slowly
evolving curvature, for which tangency of finite time stable foliations
(related to a “forward time” perspective) and finite time unstable foliations
(related to a “backwards time” perspective) serve a central role. We compare
and contrast this perspective to both the variational method of geodesics [17],
as well as the coherent pairs perspective [12] from transfer operators.
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