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

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

2008-04-05

arxiv.org/abs/0804.0860v1

Mathematics

Dynamical Systems

53 pages

Scientific paper

We introduce a notion of super-potential (canonical function) associated to positive closed (p,p)-currents on compact Kaehler 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 the regularity, the entropy, the ergodicity and the hyperbolicity of the equilibrium measures.

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