On the regularity of the Green current for semi-extremal endomorphisms of $ {P}^2 $

Christophe Dupont (1) , Axel Rogue (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We study the regularity of the Green current for semi-extremal endomorphisms of P-2. Under suitable assumptions, we show that the point-wise lower Radon-Nikodym derivative of stable slices with respect to the one dimensional Lebesgue measure is bounded at almost every point for the equilibrium measure. This provides a weak amount of metric regularity for the Green current along holomorphic discs.

Mots clés: Holomorphic dynamics; Lyapunov exponents; Green current

Domaines: Systèmes dynamiques [math.DS]

Christophe Dupont, Axel Rogue. On the regularity of the Green current for semi-extremal endomorphisms of $ {P}^2 $. Discrete & Continuous Dynamical Systems - A, 2020, Conference on Dynamics, Equations and Applications (DEA), 40 (12), pp.6767-6781. ⟨10.3934/dcds.2020163⟩. ⟨hal-02936357⟩