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On the numerical approximation of the Perron-Frobenius and Koopman operator

  • Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the Perron-Frobenius and the Koopman operator. In this paper, we will review di� fferent methods that have been developed over the last decades to compute � infinite-dimensional approximations of these in� finite-dimensional operators - in particular Ulam's method and Extended Dynamic Mode Decomposition (EDMD) - and highlight the similarities and di� fferences between these approaches. The results will be illustrated using simple stochastic di� fferential equations and molecular dynamics examples.

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Author:Stefan Klus, Peter Koltai, Christof Schütte
Document Type:Article
Parent Title (English):Journal of Computational Dynamics
First Page:51
Last Page:77
Year of first publication:2016