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

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arxiv 1512.05997 v3 pith:LTSVVI2J submitted 2015-12-18 math.DS cs.NAmath.NA

Stefan Klus , Péter Koltai , Christof Schütte This is my paper · ORCID
classification math.DScs.NAmath.NA
keywords operatorsdynamicalexampleskoopmanoperatorperron-frobeniuswillanalyzing
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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 different methods that have been developed over the last decades to compute finite-dimensional approximations of these infinite-dimensional operators - e.g. Ulam's method and Extended Dynamic Mode Decomposition (EDMD) - and highlight the similarities and differences between these approaches. The results will be illustrated using simple stochastic differential equations and molecular dynamics examples.

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