A normal form of completely integrable systems
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文摘
The purpose of this article is to show that a differential system on which admits a set of independent conservation laws defined on an open subset , is essentially equivalent on an open and dense subset of , with the linear differential system . 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.