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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
70/2015

Characterization of Exact Lumpability of Smooth Dynamics on Manifolds

Leonhard Horstmeyer and Fatihcan M. Atay

Abstract

We characterize the exact lumpability of nonlinear differential equations on smooth manifolds. We derive necessary and sufficient conditions for lumpability and express them from four different perspectives, thus simplifying and generalizing various results from the literature that exist for Euclidean spaces. The conditions are formulated in terms of the differential of the lumping map, its Lie derivative, and their respective kernels. Two examples are discussed to illustrate the theory.

Received:
Oct 27, 2015
Published:
Oct 27, 2015
MSC Codes:
34C4, 34C20, 37J15
PACS:
02.30.Hq, 02.30.Ik, 02.30.Yy
Keywords:
lumping, aggregation, dimensional reduction

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Preprint
2015 Repository Open Access
Leonhard Horstmeyer and Fatihcan M. Atay

Characterization of exact lumpability of smooth dynamics on manifolds