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We introduce a notion of super-potential (canonical function) associated topositive closed (p,p)-currents on compact Kaehler manifolds and we develop acalculus on such currents. One of the key points in our study is the use ofdeformations in the space of currents. As an application, we obtain severalresults on the dynamics of holomorphic automorphisms: regularity and uniquenessof the Green currents. We also get the regularity, the entropy, the ergodicityand the hyperbolicity of the equilibrium measures.

Super-potentials for currents on compact Kähler manifolds and dynamics of automorphisms