Characterization of Exact Lumpability of Smooth Dynamics on Manifolds
Leonhard Horstmeyer and Fatihcan M. Atay
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Submission date: 27. Oct. 2015
MSC-Numbers: 34C4, 34C20, 37J15
PACS-Numbers: 02.30.Hq, 02.30.Ik, 02.30.Yy
Keywords and phrases: lumping, aggregation, dimensional reduction
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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.