Integrability and Non Integrability of Some n Body Problems

Thierry Combot 1, *
* Auteur correspondant
1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
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.
Keywords : Homogeneous potential Central configurations Morales-Ramis theory Differential Galois theory Integrable systems
Type de document :
Chapitre d'ouvrage
Bernard Bonnard ; Monique Chyba Recent Advances in Celestial and Space Mechanics, 23, Springer International Publishing, pp.1-30, 2016, Mathematics for Industry, 978-3-319-27462-1, 978-3-319-27464-5. 〈10.1007/978-3-319-27464-5_1〉
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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 : vendredi 8 juin 2018 - 14:50:07

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Thierry Combot. Integrability and Non Integrability of Some n Body Problems. Bernard Bonnard ; Monique Chyba Recent Advances in Celestial and Space Mechanics, 23, Springer International Publishing, pp.1-30, 2016, Mathematics for Industry, 978-3-319-27462-1, 978-3-319-27464-5. 〈10.1007/978-3-319-27464-5_1〉. 〈hal-01514125〉

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