Non-integrability of the equal mass n-body problem with non-zero angular momentum |
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| Authors: | Thierry Combot |
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| Institution: | 1. IMCCE, 77 Avenue Denfert Rochereau, 75014, Paris, France
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| Abstract: | We prove an integrability criterion and a partial integrability criterion for homogeneous potentials of degree ?1 which are invariant by rotation. We then apply it to the proof of the meromorphic non-integrability of the n-body problem with Newtonian interaction in the plane on a surface of equation (H, C) = (H 0, C 0) with (H 0, C 0) ?? (0, 0) where C is the total angular momentum and H the Hamiltonian, in the case where the n masses are equal. Several other cases in the 3-body problem are also proved to be non integrable in the same way, and some examples displaying partial integrability are provided. |
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