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

TL;DR

This paper proves the existence of complex carousel solutions in the planar N-body problem, where clusters of bodies move near central configurations, using advanced variational blow-up techniques.

Contribution

It introduces a new class of solutions called carousel solutions, extending previous work by constructing them from clusters near central configurations.

Findings

Existence of carousel solutions in the N-body problem.

Methodology based on blow-up techniques for variational methods.

Extension of previous results to clustered 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.