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

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 \mathb…