Periodic orbits of the restricted three-body problem

Mathlouthi, Salem

doi:10.1090/S0002-9947-98-01731-0

Periodic orbits of the restricted three-body problem
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by Salem Mathlouthi

Trans. Amer. Math. Soc. 350 (1998), 2265-2276

DOI: https://doi.org/10.1090/S0002-9947-98-01731-0

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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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