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Contrast of Perspectives of Coherency

Contrast of Perspectives of Coherency
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摘要 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. 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.
出处 《Journal of Applied Mathematics and Physics》 2015年第7期781-791,共11页 应用数学与应用物理(英文)
关键词 Shape COHERENT Set COHERENT Pairs GEODESIC TRANSPORT Barrier Finite-Time Stable and Unstable FOLIATIONS Implicit Function Theorem CONTINUATION Mixing TRANSPORT Shape Coherent Set Coherent Pairs Geodesic Transport Barrier Finite-Time Stable and Unstable Foliations Implicit Function Theorem Continuation Mixing Transport
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