On a unified formulation of completely integrable systems

Details On a unified formulation of completely integrable systems On a unified formulation of completely integrable systems

2011-06-24

arxiv.org/abs/1106.5044v4

Journal of Geometry and Physics, 62(5)(2012), 1167-1174

Mathematics

Dynamical Systems

11 pages

Scientific paper

The purpose of this article is to show that a $\mathcal{C}^1$ differential system on $\R^n$ which admits a set of $n-1$ independent $\mathcal{C}^2$ conservation laws defined on an open subset $\Omega\subseteq \R^n$, is essentially $\mathcal{C}^1$ equivalent on an open and dense subset of $\Omega$, with the linear differential system $u^\prime_1=u_1, \ u^\prime_2=u_2,..., \ u^\prime_n=u_n$. 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.

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