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Transactions of the American Mathematical Society

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

 

 

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
DOI: https://doi.org/10.1090/S0002-9947-98-01731-0
MathSciNet review: 1373645
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Abstract | References | Similar Articles | Additional Information

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

DOI: https://doi.org/10.1090/S0002-9947-98-01731-0
Received by editor(s): July 20, 1995
Article copyright: © Copyright 1998 American Mathematical Society