Tian Ma, Erik Bollt

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Department of Mathematics and Computer Science, Clarkson University, Potsdam, NY, USA.
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Abstract: 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.

Keywords: Shape Coherent Set, Coherent Pairs, Geodesic Transport Barrier, Finite-Time Stable and Unstable Foliations, Implicit Function Theorem, Continuation, Mixing, Transport

Cite this paper: Ma, T. and Bollt, E. (2015) Contrast of Perspectives of Coherency. Journal of Applied Mathematics and Physics, 3, 781-791. doi: 10.4236/jamp.2015.37095.

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