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Symmetric periodic orbits in three sub-problems of the $N$-body problem

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  • We study three sub-problems of the $N$-body problem that have two degrees of freedom, namely the $n-$pyramidal problem, the planar double-polygon problem, and the spatial double-polygon problem. We prove the existence of several families of symmetric periodic orbits, including ``Schubart-like" orbits and brake orbits, by using topological shooting arguments.
    Mathematics Subject Classification: Primary: 70F07; Secondary: 37C27.


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