Non-integrability of the $n$-body problem
Mathematical Physics
2025-05-27 v2 math.MP
Abstract
We prove that the classical planar -body problem when restricted to a common level of the energy and the angular momentum is not integrable except in the case when both values of these integrals are zero. In the proof of our theorem, we use methods of differential Galois theory.
Cite
@article{arxiv.2502.01426,
title = {Non-integrability of the $n$-body problem},
author = {Andrzej J. Maciejewski and Maria Przybylska and Thierry Combot},
journal= {arXiv preprint arXiv:2502.01426},
year = {2025}
}
Comments
33 pages, accepted for publication in in the Journal of the European Mathematical Society