%0 Journal Article
%T Contrast of Perspectives of Coherency
%A Tian Ma
%A Erik Bollt
%J Journal of Applied Mathematics and Physics
%P 781-791
%@ 2327-4379
%D 2015
%I Scientific Research Publishing
%R 10.4236/jamp.2015.37095
%X <p class=\"MsoNormal\">
	<span lang=\"EN-US\">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 ˇ°shape coherent setsˇ± which is proven to correspond to slowly
evolving curvature, for which tangency of finite time stable foliations
(related to a ˇ°forward timeˇ± perspective) and finite time unstable foliations
(related to a ˇ°backwards timeˇ± 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.</span> 
</p>
%K Shape Coherent Set
%K Coherent Pairs
%K Geodesic Transport Barrier
%K Finite-Time Stable and Unstable Foliations
%K Implicit Function Theorem
%K Continuation
%K Mixing
%K Transport
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=57640