Stability in Hamiltonian systems : applications to the restricted three-body problem

Abstract

The N-body problem is a classical famous problem which has attracted a lot of attention. It consists of describing the complete behavior of all solutions of the equations of motions for a given initial condition. Still related to this kind of problem Euler in 1772 describe the three-body problem in his eort to study the motion of the moon. Later on Jacobi in 1836 brought forward the main mathematical interest in an even more specic part of the three body problem, namely the one which is reduced to a conservative two degrees of freedom problem. This has somehow brought up an extensive study on mechanics. Despite of all this eort of great mathematicians, in general the N-body problem for N> 2 is still unsolved.