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Non-integrability of the -body problem

  • Andrzej J. Maciejewski

    University of Zielona Góra, Poland
    ORCID

  • Maria Przybylska

    University of Zielona Góra, Poland
    ORCID

  • Thierry Combot

    Université de Burgogne, Dijon, France
Non-integrability of the $n$-body problem cover

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Abstract

We prove that the classical planar -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.

Cite this article

Andrzej J. Maciejewski, Maria Przybylska, Thierry Combot, Non-integrability of the -body problem. J. Eur. Math. Soc. (2025), published online first

DOI 10.4171/JEMS/1717