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Chapitre d'ouvrage
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.
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 : mardi 10 novembre 2020 - 17:14:04
Contributeur : Ub_drive Université de Bourgogne <>
Soumis le : mardi 25 avril 2017 - 17:09:03
Dernière modification le : mardi 10 novembre 2020 - 17:14:04
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