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arXiv · 2404.17500

A note on the rational non-integrability of the $N$-center problem for almost all degrees of the singularities

Eddaly Guerra-Velasco·Boris Percino-Figueroa·Russell-Aarón Quiñones-Estrella
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Abstract

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.

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Eddaly Guerra-Velasco, Boris Percino-Figueroa, Russell-Aarón Quiñones-Estrella. 2024-10-03. A note on the rational non-integrability of the $N$-center problem for almost all degrees of the singularities. https://arxiv.org/abs/2404.17500

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