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Periodic orbits of the restricted three-body problem

Author: Salem Mathlouthi
Journal: Trans. Amer. Math. Soc. 350 (1998), 2265-2276
MSC (1991): Primary 34A34; Secondary 34A47
MathSciNet review: 1373645
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Abstract: 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
Article copyright: © Copyright 1998 American Mathematical Society