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math.DSSep 26, 2000
13
citations (OpenAlex)
authors
  • Alexei Tsygvintsev
institutions
  • Centre National de la Recherche Scientifique
  • Institut de Mathématiques de Toulouse
  • Université Toulouse III - Paul Sabatier
  • University of Geneva
arXiv abstractPDF
paper

The meromorphic non-integrability of the planar three-body problem

arXiv:math/0009217 · doi:10.1016/S0764-4442(00)01623-2

Abstract

We study the planar three-body problem and prove the absence of a complete set of complex meromorphic first integrals in a neighborhood of the Lagrangian solution.

4 pages, French

Cited by in corpus (2)

  • Non-integrability of the problem of a rigid satellite in gravitational and magnetic fields
  • On some exceptional cases in the integrability of the three-body problem
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