A non-laminar Green current

Romain Dujardin (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

A holomorphic endomorphism f of CP2 admits a Julia set J1, defined as usual to be the locus of non-normality of its iterates (fn)n≥0, and a (typically) smaller Julia set J2, which is essentially the closure of the set of repelling periodic orbits. The question has been raised whether J1 \ J2 is filled (possibly in a measure-theoretic sense) with "Fatou subvarieties" along which the dynamics is locally equicontinuous. In this article we construct examples showing that this is not the case in general.

Domaines: Systèmes dynamiques [math.DS]

Romain Dujardin. A non-laminar Green current. Mathematische Annalen, 2016, 365, pp.77-91. ⟨hal-01068577⟩