Abstract
The purpose of this article is to show that a C1 differential system on Rn which admits a set of n−1 independent C2 conservation laws defined on an open subset Ω⊆Rn, is essentially C1 equivalent on an open and dense subset of Ω, with the linear differential system u1′=u1,u2′=u2,…,un′=un. The main results are illustrated in the case of two concrete dynamical systems, namely the three dimensional Lotka–Volterra system, and respectively the Euler equations from the free rigid body dynamics.
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