Differential Galois obstructions for non-commutative integrability

Details Differential Galois obstructions for non-commutative integrability Differential Galois obstructions for non-commutative integrability

2007-01-30

arxiv.org/abs/nlin/0701061v1

Phys. Lett. A., vol 372, no 33, 5431--5435, (2008)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

submitted to Journal of Geometry and Physics

Scientific paper

10.1016/j.physleta.2008.06.050

We show that if a holomorphic Hamiltonian system is holomorphically integrable in the non-commutative sense in a neighbourhood of a non-equilibrium phase curve which is located at a regular level of the first integrals, then the identity component of the differential Galois group of the variational equations along the phase curve is Abelian. Thus necessary conditions for the commutative and non-commutative integrability given by the differential Galois approach are the same.

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