Non-integrability of the $n$-body problem
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913856865959936 |
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| author | Maciejewski, Andrzej J. Przybylska, Maria Combot, Thierry |
| author_facet | Maciejewski, Andrzej J. Przybylska, Maria Combot, Thierry |
| contents | We prove that the classical planar $n$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-integrability of the $n$-body problem Maciejewski, Andrzej J. Przybylska, Maria Combot, Thierry Mathematical Physics 70F10, 37N05 We prove that the classical planar $n$-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. |
| title | Non-integrability of the $n$-body problem |
| topic | Mathematical Physics 70F10, 37N05 |
| url | https://arxiv.org/abs/2502.01426 |