English

Liouville integrability: an effective Morales-Ramis-Sim\'o theorem

Classical Analysis and ODEs 2021-08-25 v2

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-Sim\'o criterion for testing meromorphic Liouville integrability of Hamiltonian systems.

Keywords

Cite

@article{arxiv.1505.02808,
  title  = {Liouville integrability: an effective Morales-Ramis-Sim\'o theorem},
  author = {Ainhoa Aparicio-Monforte and Thomas Dreyfus and Jacques-Arthur Weil},
  journal= {arXiv preprint arXiv:1505.02808},
  year   = {2021}
}

Comments

29 pages

R2 v1 2026-06-22T09:32:14.635Z