We introduce a notion of super-potential for positive closed currents of bidegree (p, p) on projective spaces. This gives a calculus on positive closed currents of arbitrary bidegree. We define in particular the intersection of such currents and the pull-back operator by meromorphic maps. One of the main tools is the introduction of structural discs in the space of positive closed currents which gives a "geometry" on that space. We apply the theory of super-potentials to construct Green currents for rational maps and to study equidistribution problems for holomorphic endomorphisms and for polynomial automorphisms.

Let X be a complex projective manifold and let f be a dominating rational map from X onto X. We show that the topological entropy h(f ) of f is bounded from above by the logarithm of its maximal dynamical degree.

Abstract.A meromorphic transform (MT) between compact Kähler manifolds is a surjective multivalued map with an analytic graph. Let F n : X → X n be a sequence of MT. Let σ n be an appropriate probability measure on X n and σ the product measure of σ n , on X := n≥1 X n . We give conditions which imply that We also construct the equilibrium measure for random iteration of correspondences. In particular, when f : X → X is a meromorphic correspondence of large topological degree d t , we show that d −n t (f n ) * ω k converges to a measure μ, satisfying f * μ = d t μ. Moreover, quasipsh functions are μ-integrable. Every projective manifold admits such correspondences. When f is a meromorphic map, μ is exponentially mixing with a precise speed depending on the regularity of the observables. Mathematics Subject Classification (2000). 32H, 37D, 37A25, 81Q50.Keywords. Meromorphic correspondences, dynamical degrees, speed of mixing, random polynomials. (X, ω, σ, t) Notations. Dans tout l'article (X, ω), (X , ω ) et (X n , ω n ) désignent des varié-tés kählériennes compactes de dimensions respectives