Invariance and the n-body problem

The N-body Problem

The quantum N-body problem

This selective review is written as an introduction to the mathematical theory of the Schro ̈dinger equation for N particles. Characteristic for these systems are the cluster properties of the potential in configuration space, which are expressed in a simple geometric language. The methods developed over the last 40 years to deal with this primary aspect are described by giving full proofs of...

Array languages and the N-body problem

Unchained polygons and the N-body problem

We study both theoretically and numerically the Lyapunov families which bifurcate in the vertical direction from a horizontal relative equilibrium in R. As explained in [CF1], very symmetric relative equilibria thus give rise to some recently studied classes of periodic solutions. We discuss the possibility of continuing these families globally as action minimizers in a rotating frame where the...

The N-Membranes Problem