On a unified formulation of completely integrable systems

Abstract

The purpose of this article is to show that a ${\mathcal{C}}^1$ differential system on ${\mathbb{R}}^n$ which admits a set of $n-1$ independent ${\mathcal{C}}^2$ conservation laws defined on an open subset $\Omega \subseteq {\mathbb{R}}^n$, is essentially ${\mathcal{C}}^1$ equivalent on an open and dense subset of $\Omega$, with the linear differential system $u_1^{\prime }=u_1,u_2^{\prime }=u_2,...,u_n^{\prime }=u_n$. 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.

11 pages

References in corpus (1)

• Dynamical Systems and Poisson Structures

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