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Regularization of currents and entropy
Abstract Let T be a positive closed ( p , p ) -current on a compact Kahler manifold X. We prove the existence of smooth positive closed ( p , p ) -forms T n + and T n − such that T n + − T n − → TExpand
Attracting current and equilibrium measure for attractors on ℙk
Let f be a holomorphic endomorphism of ℙk having an attracting setA. We construct an attracting current and an equilibrium measure associated toA. The attracting current is weakly laminar andExpand
Green currents for holomorphic automorphisms of compact Kähler manifolds
and some additional regularity properties. Very likely, the currents T will describe the distribution of invariant manifolds of codimension s corresponding to the small est Lyapounov exponents. LetExpand
Super-potentials of positive closed currents, intersection theory and dynamics
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 inExpand
Dynamics in Several Complex Variables: Endomorphisms of Projective Spaces and Polynomial-like Mappings
The emphasis of this introductory course is on pluripotential methods in complex dynamics in higher dimension. They are based on the compactness properties of plurisubharmonic (p.s.h.) functions andExpand
Equidistribution towards the Green current for holomorphic maps
Soient f un endomorphisme holomorphe non-inversible d'un espace projectif et f n son itere d'ordre n. Nous prouvons que l'image reciproque par f n d'une hypersurface generique (au sens de Zariski),Expand
Let f be a dominant meromorphic self-map on a compact Kahler manifold X which preserves a meromorphic fibration π : X → Y of X over a compact Kahler manifold Y. We compute the dynamical degrees of fExpand
Rigidity of Julia sets for Henon type maps
We prove that the Julia set of a Henon type automorphism on C^2 is very rigid: it supports a unique positive ddc-closed current of mass 1. A similar property holds for the cohomology class of theExpand
Super-potentials for currents on compact Kähler manifolds and dynamics of automorphisms
We introduce a notion of super-potential (canonical function) associated to positive closed (p, p)-currents on compact Kahler manifolds and we develop a calculus on such currents. One of the keyExpand