Absolute continuity for semi-extremal holomorphic mappings

Absolue continuité pour les applications holomorphes semi-extrémales

Virgile Tapiero (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We study the equilibrium measure µ = T ∧ T of endomorphisms f of CP(2) of degree d ≥ 2, where T is the Green current of f. Dujardin proved that if µ is absolutely continuous with respect to T then f has a minimal Lyapunov exponent [12]. We show the reverse implication under a local uniform assumption on unstable manifolds of the dynamical system.

Mots clés: Equilibrium measure; Green current; Lyapunov exponents; normal forms; measurable partition; entropy

Domaines: Systèmes dynamiques [math.DS]; Variables complexes [math.CV]

Virgile Tapiero. Absolute continuity for semi-extremal holomorphic mappings. 2022. ⟨hal-03878896⟩