Non-integrability of the $n$-body problem
Year: 2025
Type: article
Abstract: We prove that the classical planar n -body problem when restricted to a common level of the energy and the angular momentum is not integrable except in the case when both values of these first integrals are zero. In the proof of our theorem, we use methods of differential Galois theory.
DOI: 10.4171/jems/1717
Institutions: University of Zielona Góra, Université de Bourgogne
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7082287568