T.Kapela, N-BODY choreographies with a reflectional symmetry - computer assisted existence proofs

We proof the existence of symmetric choreographies - solutions of the planar N-body problem on which all bodies travel on the same curve. We describe general method of computer assisted proofs using reflectional symmetry of the orbit to isolate a solution. Using this method we proved, as an example, the existence of many choreographies of 4 and 5 bodies.

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