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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.17500 |
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Table of 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.