A distortion theorem for the iterated inverse branches of a holomorphic endomorphism of CP(k)

François Berteloot (1) , Christophe Dupont (2)

1 LEP - Laboratoire Émile Picard
2 IRMAR - Institut de Recherche Mathématique de Rennes

We linearize the inverse branches of the iterates of holomorphic endomorphisms of CP(k) and thus overcome the lack of Koebe distortion theorem in this setting when k ≥ 2. We review several applications of this result in holomorphic dynamics.

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

François Berteloot, Christophe Dupont. A distortion theorem for the iterated inverse branches of a holomorphic endomorphism of CP(k). Journal of the London Mathematical Society, 2019, 99 (1), pp.153-172. ⟨10.1112/jlms.12163⟩. ⟨hal-01616960⟩