The study of the dynamics of n point masses interacting according to Newtonian gravity is usually called the n-body problem. It can be considered as old as the history of the science and has influenced most of the areas in mathematics. However, most of the problems in Celestial Mechanics are beyond the present limits of the knowledge and many natural questions are difficult or impossible to solve when the number of bodies n is larger than 2.
In order to make progress against such complexity one must look for specific objects. From a geometrical point of view a key point consists in trying to understand the structure of the phase space looking for the equilibrium points, periodic orbits, invariant tori, ... The stable and unstable manifolds associated to these objects form a kind of network of connections, which together with the previous invariants objects constitute a big part of the main skeleton of the system.
One of the main ingredients of the phase space are the periodic orbits. Over the years, many authors have contributed to study the periodic orbits of a wide variety of n-body problems from different points of view. A particular interesting type of periodic orbit in the planar n-body problem is one in which the particles remain in the same shape relative to one another. The possible configurations for the particles in such orbits are called central configurations.
The purpose of this research programme is finding new approaches to the main open questions in the following topics: First to central configurations (mainly for few bodies), and second to periodic orbits of the n-body problem and their bifurcations.