. D G ] 1 5 Se p 20 07 Ricci iterations on Kähler classes

In this paper we consider the dynamical system involved by the Ricci operator on the space of Kähler 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 KählerEinstein manifold. In particular we show that the iterates do converge to the Kähler-Ricci soliton for toric manifolds. Finally, we define a finite dimensional procedure to give an approximation of Kähler-Einstein metrics using this iterative procedure and apply it for P blown up in 3 points.