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Title:Choreographies and braids in the n-body problem.

Abstract: In this talk, we present a summary of results about the existence of periodic solutions for n bodies that are known as choreographies and braids. In the second part of the talk, we explain how to obtain the existence of a special type of braid solutions where one body in a central configuration of n bodies is replaced by a pair of bodies rotating uniformly around its center of mass. In these solutions n−1 bodies and the center of mass of the pair winds around the origin q times, while the pair of bodies winds around its center of mass p times. The proof uses blow-up techniques to separate the (n+1)-body problem as the n-body problem, the Kepler problem, and a coupling which is small if the distance of the pair is small. The formulation is variational and the result is obtained by applying a Lyapunov-Schmidt reduction and the use of the equivariant Lyusternik-Schnirelmann category.