Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On integrability of the Kontsevich non-abelian ODE system   We consider systems of ODEs with the right hand side being Laurent
polynomials in several non-commutative unknowns. In particular, these unknowns
could be matrices of arbitrary size. An important example of such a system was
proposed by M. Kontsevich. We prove the integrability of the Kontsevich system
by finding a Lax pair, corresponding first integrals and commuting flows. We
also provide a pre-Hamiltonian operator which maps gradients of integrals for
the Kontsevich system to symmetries.

20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th