Characterization of Exact Lumpability of Smooth Dynamics on Manifolds

Leonhard Horstmeyer and Fatihcan M. Atay

Contact the author: Please use for correspondence this email.
Submission date: 27. Oct. 2015
Pages: 19
Bibtex
MSC-Numbers: 34C4, 34C20, 37J15
PACS-Numbers: 02.30.Hq, 02.30.Ik, 02.30.Yy
Keywords and phrases: lumping, aggregation, dimensional reduction
Download full preprint: PDF (407 kB)

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.