Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a unified formulation of completely integrable systems   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.

16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ