The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
On the numerical approximation of the Perron-Frobenius and Koopman operator
Open accessAbstract
Information about the behavior of dynamical systems can oftenbe obtained by analyzing the eigenvalues and corresponding eigenfunctions oflinear operators associated with a dynamical system. Examples of such operatorsare the Perron-Frobenius and the Koopman operator. In this paper, wewill review di erent methods that have been developed over the last decades tocompute nite-dimensional approximations of these in nite-dimensional operators- in particular Ulam's method and Extended Dynamic Mode Decomposition(EDMD) - and highlight the similarities and di erences between theseapproaches. The results will be illustrated using simple stochastic di erentialequations and molecular dynamics examples.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Lasota, A., & Mackey, M. C. (1994) · Applied Mathematical Sciences · doi:10.1007/978-1-4612-4286-4 · Cited by 1,353
A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems
Noé, F., & Nüske, F. (2013) · Multiscale Modeling & Simulation · doi:10.1137/110858616 · Cited by 327 · cited 2×
“This results in a method similar to the variational approach presented in [42] for reversible processes.”
MethodResultVariational approach to molecular kinetics
Nüske, F., Keller, B. G., Pérez-Hernández, G., Mey, A. S. J. S., & Noé, F. (2014) · Journal of Chemical Theory and Computation · doi:10.1021/ct4009156 · Cited by 308
How well-connected is the surface of the global ocean?
Froyland, G., Stuart, R. M., & van Sebille, E. (2014) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4892530 · Cited by 131
Cited by
Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
Korda, M., & Mezić, I. (2018) · Automatica · doi:10.1016/j.automatica.2018.03.046 · Cited by 1,157
Klus, S., Nüske, F., Peitz, S., Niemann, J.-H., Clementi, C., & Schütte, C. (2020) · Physica D: Nonlinear Phenomena · doi:10.1016/j.physd.2020.132416 · Cited by 267
Self-citationIdentifying Efficient Ensemble Perturbations for Initializing Subseasonal‐To‐Seasonal Prediction
Demaeyer, J., Penny, S. G., & Vannitsem, S. (2022) · Journal of Advances in Modeling Earth Systems · doi:10.1029/2021ms002828 · Cited by 9
Metadata
- Authors
- Klus, S., Koltai, P., & Schütte, C.
- Venue
- Journal of Computational Dynamics
- Published
- 2016
- Volume
- 3
- Issue
- 1
- Pages
- 51-79
- ISSN
- 2158-2491 (ISSN-L)
- 2158-2505
- OpenAlex
- W2267246336
- Cited by
- 179
- References
- 4
- FWCI
- 4.99
- Type
- journal article
- Language
- en
- Open access
- diamond
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: On the numerical approximation of the Perron-Frobenius and Koopman operator. https://app.cochat.ai/papers/10.3934/jcd.2016003
- The paper
- Klus, S., Koltai, P., & Schütte, C. (2016). On the numerical approximation of the Perron-Frobenius and Koopman operator. Journal of Computational Dynamics. https://doi.org/10.3934/jcd.2016003
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
