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

Full text not available from this repository.

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 |

Repository Staff Only: item control page