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

Abstract

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.

53 pages

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Cited by in corpus (8)

• Equidistribution of saddle periodic points for Henon-type automorphisms of C^k
• Least negative intersections of positive closed currents on compact Kähler manifolds
• Strong submeasures and several applications
• Densities of currents and complex dynamics
• The g-periodic subvarieties for an automorphism g of positive entropy on a compact Kahler manifold
• An explicit Koppelman formula for $d{d}^c$ and Green currents on ${\mathcal{P}}^n$
• The Monge-Ampere operator of some singular (1,1) currents coming from pseudo-isomorphisms in dimension $3$
• Exponential mixing for automorphisms on compact Kaehler manifolds