  In this paper we consider the dynamical system involved by the Ricci operator
on the space of K\"ahler metrics. A. Nadel has defined an iteration scheme
given by the Ricci operator for Fano manifold and asked whether it has some
nontrivial periodic points. First, we prove that no such periodic points can
exist. We define the inverse of the Ricci operator and consider the dynamical
behaviour of its iterates for a Fano K\"ahler-Einstein manifold. In particular
we show that the iterates do converge to the existing K\"ahler-Ricci soliton on
a toric manifold. Finally, we define a finite dimensional procedure to give an
approximation of K\"ahler-Einstein metrics using this iterative procedure and
apply it for $\mathbb{CP}^2$ blown up in 3 points.
