Integrability and Non Integrability of Some n Body Problems

Abstract : We prove the non integrability of the colinear 3 and 4 body problem, for any positive masses. To deal with resistant cases, we present strong integrability criterions for 3 dimensional homogeneous potentials of degree −1, and prove that such cases cannot appear in the 4 body problem. Following the same strategy, we present a simple proof of non integrability for the planar n body problem. Eventually, we present some integrable cases of the n body problem restricted to some invariant vector spaces.
Liste complète des métadonnées

https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01514125
Contributeur : Ub_drive Université de Bourgogne <>
Soumis le : mardi 25 avril 2017 - 17:09:03
Dernière modification le : jeudi 11 janvier 2018 - 06:12:20

Lien texte intégral

Identifiants

Collections

Partager

Métriques

Consultations de la notice

62