A note on the rational non-integrability of the $N$-center problem for almost all degrees of the singularities
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912056104452096 |
|---|---|
| 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 |