  We consider the radial energy-critical non-linear focusing Schr\"odinger
equation in dimension N=3,4,5. An explicit stationnary solution, W, of this
equation is known. In a previous work by C. Carlos and F. Merle, the energy
E(W) has been shown to be a threshold for the dynamical behavior of solutions
of the equation. In the present article, we study the dynamics at the critical
level E(u)=E(W) and classify the corresponding solutions. This gives in
particular a dynamical characterization of W.
