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.
Author: | Stefan Klus, Peter Koltai, Christof Schütte |
---|---|
Document Type: | Article |
Parent Title (English): | Journal of Computational Dynamics |
Volume: | 3 |
Issue: | 1 |
First Page: | 51 |
Last Page: | 77 |
Year of first publication: | 2016 |
DOI: | https://doi.org/10.3934/jcd.2016003 |