Repository: Freie Universität Berlin, Math Department

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

Klus, S. and Koltai, Péter and Schütte, Ch. (2016) On the numerical approximation of the Perron-Frobenius and Koopman operator. Journal of Computational Dynamics, 3 (1). pp. 51-79. ISSN 2158-2491

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Official URL: http://www.aimsciences.org/journals/displayArticle...

Abstract

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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
ID Code:1774
Deposited By: Ulrike Eickers
Deposited On:26 Jan 2016 09:56
Last Modified:20 Jan 2017 09:57

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