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| Using the variational method, Chenciner and Montgomery proved the existence of an eight-shaped periodic solution of the planar three-body problem with equal masses. Just after the discovery, Gerver have numerically found a similar periodic solution called ``super-eight'' in the planar four-body problem with equal mass.
In this talk I will prove the existence of the super-eight orbit by using the variational method. The difficulty of the proof is to eliminate the possibility of collisions. In order to solve it, we apply the scaling technique established by Tanaka and investigate the asymptotic behavior of a binary collision. |
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