Liouville integrability: an effective Morales-Ramis-Simó theorem
arXiv:1505.02808 · doi:10.1016/j.jsc.2015.08.009
Abstract
Consider a complex Hamiltonian system and an integral curve. In this paper, we give an effective and efficient procedure to put the variational equation of any order along the integral curve in reduced form provided that the previous one is in reduced form with an abelian Lie algebra. Thus, we obtain an effective way to check the Morales-Ramis-Simó criterion for testing meromorphic Liouville integrability of Hamiltonian systems.
29 pages
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Cited by in corpus (4)
- Computing the Lie algebra of the differential Galois group: the reducible case
- Galoisian Methods for Testing Irreducibility of Order Two Nonlinear Differential Equations
- Darboux Transformations for Orthogonal Differential Systems and Differential Galois Theory
- Necessary and sufficient conditions for meromorphic integrability near a curve