Simple choreography solutions of the Newtonian N-body Problem

Guowei Yu

Published 2015-09-16Version 1

In $N$-body problem, a simple choreography solution is a periodic solution in which all the masses chase each other on a single loop. In this paper we prove that for the Newtonian $N$-body problem, $N \ge 3$, there are at least $2^{N-2}$ different main simple choreography solutions. As a result this confirms a conjecture given by Chenciner and etc.