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\title{Efficient Approximation of Coherent Pairs}
\author{} \tocauthor{C. Horenkamp} \institute{}
{\large \underline{Christian Horenkamp}}\\
University of Paderborn\\
\\ \vspace{4mm}{\large Michael Dellnitz}\\
University of Paderborn\\
Transport phenomena in non-autonomous dynamical systems appear in a variety of applications e.g. the transport of water mass induced by eddies in the oceanic fluid flow.In order to treat transport phenomena of non-autonomous dynamical systems so-called transfer operator methods have been developed in the last years. For instance a method for the detection of so-called coherent pairs, which represent slowly mixing structures, has been introduced by Froyland et al. \cite{FroSanMon10}. These transfer operator methods have in common that they involve long term simulations of trajectories on the whole state-space which are computationally expensive. In principle the method of Froyland et al. can be applied to a subpart of the state-space which contains one of the sets of a coherent pair. If the transport process is slow enough we show that transport phenomena over a fixed (long) time horizon imply the existence of almost invariant sets over shorter time intervals. In this talk we use this fact to formulate an algorithm that preselects a part of the state-space as a candidate containing one of the sets of a coherent pair and therefore significantly reduces the related numerical effort.
{\sc G. Froyland and N. Santitissadeekorn and A. Monahan}. {Transport in time-dependent dynamical systems: Finite-time coherent sets}. Chaos, 20(4):043116, 2010.