We introduce a notion of super-potential (canonical function) associated to positive closed
(
p
,
p
)
(p,p)
-currents on compact Kähler manifolds and we develop a calculus on such currents. One of the key points in our study is the use of deformations in the space of currents. As an application, we obtain several results on the dynamics of holomorphic automorphisms: regularity and uniqueness of the Green currents. We also get regularity, entropy, ergodicity and hyperbolicity of the equilibrium measures.