Galoisian obstructions to non-Hamiltonian integrability

Michaël Ayoul; Nguyen Tien Zung

doi:10.1016/j.crma.2010.10.024

Dynamical Systems/Mathematical Problems in Mechanics

Galoisian obstructions to non-Hamiltonian integrability

Presented by: Jean-Pierre Ramis

Michaël Ayoul ¹; Nguyen Tien Zung ¹

¹ Institut de mathématiques de Toulouse, UMR 5219 CNRS, université Toulouse III, 118 route de Narbonne, 31000 Toulouse, France

Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1323-1326.

Abstract
Résumé

We show that the main theorem of Morales, Ramis and Simo (2007) [6] 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.

Nous montrons la version non-hamiltonienne du théorème de Morales, Ramis et Simo (2007) [6]. Plus précisément, si un système dynamique est méromorphiquement intégrable au sens non-hamiltonien, alors tous les groupes de Galois différentiels des équations variationelles d'ordre arbitraire le long de ses solutions doivent être virtuellement abéliens.

Received: 2010-05-04
Accepted: 2010-10-18
Published online: 2010-11-10

DOI: 10.1016/j.crma.2010.10.024

Author's affiliations:

Michaël Ayoul ¹; Nguyen Tien Zung ¹

¹ Institut de mathématiques de Toulouse, UMR 5219 CNRS, université Toulouse III, 118 route de Narbonne, 31000 Toulouse, France

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     author = {Micha\"el Ayoul and Nguyen Tien Zung},
     title = {Galoisian obstructions to {non-Hamiltonian} integrability},
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Michaël Ayoul; Nguyen Tien Zung. Galoisian obstructions to non-Hamiltonian integrability. Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1323-1326. doi : 10.1016/j.crma.2010.10.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.024/

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