DYNAMIQUE DES APPLICATIONS RATIONNELLES DES

We study the dynamics of rational mappings f of C by compactifying them in multiprojective spaces P1 × · · ·×Ps . We focus on maps of the surface P × P. We follow the approach of [Si 99] and associates to any algebraically stable f an invariant positive closed (1, 1) current. We then consider the existence of an f invariant measure using the theory of pluripositive currents, and relates it to the measure of Russsakovskii-Shiffman describing the distribution of preimages of points. Our point of view enables us to treat new classes of examples: we consider in particular polynomial skew products with varying degrees, and birational polynomial mappings of C. We also describe the compact convex set of f invariant currents for monomial and birational maps of C.