A note on the rational non-integrability of the $N$-center problem for almost all degrees of the singularities
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912056104452096 |
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| author | Guerra-Velasco, Eddaly Percino-Figueroa, Boris Quiñones-Estrella, Russell-Aarón |
| author_facet | Guerra-Velasco, Eddaly Percino-Figueroa, Boris Quiñones-Estrella, Russell-Aarón |
| contents | In this article, we show that the $N$-center problem with rational weak and moderate forces is not rationally integrable for all but a finite number of values $α\in(0,2)\cap \mathbb{Q}$, where $α$ is the order of the singularities. We identify the remaining cases and provide the necessary conditions for their integrability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17500 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the rational non-integrability of the $N$-center problem for almost all degrees of the singularities Guerra-Velasco, Eddaly Percino-Figueroa, Boris Quiñones-Estrella, Russell-Aarón Dynamical Systems 37J30, 70F15 In this article, we show that the $N$-center problem with rational weak and moderate forces is not rationally integrable for all but a finite number of values $α\in(0,2)\cap \mathbb{Q}$, where $α$ is the order of the singularities. We identify the remaining cases and provide the necessary conditions for their integrability. |
| title | A note on the rational non-integrability of the $N$-center problem for almost all degrees of the singularities |
| topic | Dynamical Systems 37J30, 70F15 |
| url | https://arxiv.org/abs/2404.17500 |