Braids of the N-body problem II: carousel solutions by cabling central configurations

Abstract

We prove the existence of relative periodic solutions of the planar $N={\sum }_{j=1}^n{k}_j$-body problem starting with $n$ bodies moving close to a non-degenerate central configuration and replacing each of them with clusters of $k_j$ bodies that move close to a small central configuration. We name these solutions carousel solutions. The proof relies on blow-up techniques for variational methods used in our previous work.

33 pages, 3 figures