Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A method to generate first integrals from infinitesimal symmetries   We propose a method to construct first integrals of a dynamical system,
starting with a given set of independent infinitesimal symmetries. In the case
of two infinitesimal symmetries, a rank two Poisson structure on the ambient
space it is found, such that the vector field that generates the dynamical
system, becomes a Poisson vector field. Moreover, the symplectic leaves and the
Casimir functions of the associated Poisson manifold are characterized.
Explicit conditions that guarantee Hamilton-Poisson realizations of the
dynamical system are also given.

18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex