Article citationsMore>>

Ding, J., Li, T.Y. and Zhou, A. (2002) Finite Approximations of Markov Operators. Journal of Computational and Applied Mathematics, 147-1, 137-152. http://dx.doi.org/10.1016/s0377-0427(02)00429-6

has been cited by the following article:

• TITLE: Contrast of Perspectives of Coherency

  AUTHORS: Tian Ma, Erik Bollt

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.3 No.7, June 30, 2015

  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.