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arXiv · 2112.11497

Open-flow mixing and transfer operators

Anna Klünker·Kathrin Padberg-Gehle·Jean-Luc Thiffeault
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Abstract

We study finite-time mixing in time-periodic open flow systems. We describe the transport of densities in terms of a transfer operator, which is represented by the transition matrix of a finite-state Markov chain. The transport processes in the open system are organized by the chaotic saddle and its stable and unstable manifolds. We extract these structures directly from leading eigenvectors of the transition matrix. We use different measures to quantify the degree of mixing and show that they give consistent results in parameter studies of two model systems.

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Anna Klünker, Kathrin Padberg-Gehle, Jean-Luc Thiffeault. 2021-12-21. Open-flow mixing and transfer operators. https://doi.org/10.1098/rsta.2021.0028

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