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A topological existence proof for the Schubart orbits in the collinear three-body problem

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  • A topological existence proof is presented for certain symmetrical periodic orbits of the collinear three-body problem with two equal masses, called Schubart orbits. The proof is based on the construction of a Wazewski set $W$ in the phase space. The periodic orbits are found by a shooting argument in which symmetrical initial conditions entering $W$ are followed under the flow until they exit $W$. Topological considerations show that the image of the symmetrical entrance states under this flow map must intersect an appropriate set of symmetrical exit states.
    Mathematics Subject Classification: 70F10, 70F15, 37N05, 70G40, 70G60, 70H12.

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