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
[Obstructions galoisiennes à l'intégrabilité non-hamiltonien]

Présenté par : 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.

Résumé
Abstract

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.

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.

Reçu le : 2010-05-04
Accepté le : 2010-10-18
Publié le : 2010-11-10

DOI : 10.1016/j.crma.2010.10.024

Affiliations des auteurs :

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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     title = {Galoisian obstructions to {non-Hamiltonian} integrability},
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     language = {en},
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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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