Galoisian obstructions to non-Hamiltonian integrability

Details Galoisian obstructions to non-Hamiltonian integrability Galoisian obstructions to non-Hamiltonian integrability

2009-01-28

arxiv.org/abs/0901.4586v1

Mathematics

Dynamical Systems

5 pages

Scientific paper

We show that the main theorem of Morales--Ramis--Simo about Galoisian obstructions to meromorphic integrability of Hamiltonian systems can be naturally extended to the non-Hamiltonian case. Namely, if a dynamical system is meromorphically integrable in the non-Hamiltonian sense, then the differential Galois groups of the variational equations (of any order) along its solutions must be virtually Abelian

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