Binary Decompositions for Planar N-Body Problems and Symmetric Periodic Solutions

A binary decomposition for a system of N masses is a way of treating the system as binaries with the total action exactly the same as that of the original system. By considering binary decompositions, we are able to provide effective lower-bound estimates for the action of collision paths in several spaces of symmetric loops. As applications, we use our estimates to prove the existence of some new classes of symmetric periodic solutions for the N-body problem.