Shooting for the Eight
A topological existence proof is given for a figure-eight periodic solution of the equal mass three-body problem. The proof is based on the construction of a Wazewski set W in the phase space. The figure-eight solution is then found by a kind of shooting argument in which symmetrical initial conditions entering W are followed under the flow until they exit W. A linking argument shows that the image of the symmetrical entrance states under this flow map must intersect an appropriate set of symmetrical exit states.
KeywordsCelestial mechanics three-body problem symmetrical periodic solutions topological methods
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