@misc{WolfEfimovskaya2011, author = {Wolf, Thomas and Efimovskaya, Olga}, title = {On integrability of the Kontsevich non-abelian ODE system}, arxiv = {http://arxiv.org/abs/1108.4208v1}, doi = {10.1007/s11005-011-0527-4}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13113}, number = {11-24}, year = {2011}, abstract = {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.}, language = {en} } @article{WolfEfimovskaya2012, author = {Wolf, Thomas and Efimovskaya, Olga}, title = {On Integrability of the Kontsevich Non-Abelian ODE System}, volume = {100}, journal = {Letters in Mathematical Physics}, number = {2}, doi = {10.1007/s11005-011-0527-4}, pages = {161 -- 170}, year = {2012}, language = {en} }