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28 March 2024
 
  » arxiv » nlin/0701061

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Differential Galois obstructions for non-commutative integrability
Andrzej J. Maciejewski ; Maria Przybylska ;
Date 30 Jan 2007
Subject Exactly Solvable and Integrable Systems
AbstractWe 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.
Source arXiv, nlin/0701061
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