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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Periodic orbits of the restricted three-body problem
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Trans. Amer. Math. Soc. 350 (1998), 2265-2276 Request permission


We prove, using a variational formulation, the existence of an infinity of periodic solutions of the restricted three-body problem. When the problem has some additional symmetry (in particular, in the autonomous case), we prove the existence of at least two periodic solutions of minimal period $T$, for every $T>0$. We also study the bifurcation problem in a neighborhood of each closed orbit of the autonomous restricted three-body problem.
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Additional Information
  • Salem Mathlouthi
  • Affiliation: Faculté des Sciences de Tunis, Département de Mathématiques, Campus Universitaire, 1060, Tunis, Tunisie
  • Received by editor(s): July 20, 1995
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 2265-2276
  • MSC (1991): Primary 34A34; Secondary 34A47
  • DOI:
  • MathSciNet review: 1373645