Local regularity of super-potentials and equidistribution of positive closed currents of ${\mathbb{P}}^k$

Abstract

In this paper, we introduce notions about local regularity of the super-potential and prove equidistribution of positive closed $(p,p)$-currents of ${\mathbb{P}}^k$ whose super-potentials are bounded near an invariant analytic subset, for holomorphic endomorphisms of ${\mathbb{P}}^k$ and for regular polynomial automorphisms of ${\mathbb{C}}^k$.

25 pages. Typos are fixed. Some proofs are corrected. arXiv admin note: text overlap with arXiv:math/0703702 by other authors

References in corpus (2)

• Value distribution for sequences of rational mappings and complex dynamics
• The Jacobian cocycle and equidistribution towards the Green current