On the numerical approximation of the Perron-Frobenius and Koopman operator
Dynamical Systems
2016-10-21 v3 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.1512.05997,
title = {On the numerical approximation of the Perron-Frobenius and Koopman operator},
author = {Stefan Klus and Péter Koltai and Christof Schütte},
journal= {arXiv preprint arXiv:1512.05997},
year = {2016}
}