On integrability of the Kontsevich non-abelian ODE system
Please always quote using this URN: urn:nbn:de:0297-zib-13113
- 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.
Author: | Thomas Wolf, Olga Efimovskaya |
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Document Type: | ZIB-Report |
Tag: | integrability, Lax pairs, noncommutative ODE, Laurent ODE |
MSC-Classification: | 34-XX ORDINARY DIFFERENTIAL EQUATIONS |
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] | |
Date of first Publication: | 2011/06/20 |
Series (Serial Number): | ZIB-Report (11-24) |
ArXiv Id: | http://arxiv.org/abs/1108.4208v1 |
ZIB-Reportnumber: | 11-24 |
Published in: | Appeared in: Lett. in Math. Phys., vol 100, no 2 (2012), p 161-170 |
DOI: | https://doi.org/10.1007/s11005-011-0527-4 |