English

A non-laminar dynamical Green current

Dynamical Systems 2014-04-18 v2 Complex Variables

Abstract

A holomorphic endomorphism f of CP^2 admits a Julia set J_1, defined as usual to be the locus of non-normality of its iterates, and a (typically) smaller Julia set J_2, which is essentially the closure of the set of repelling periodic orbits. The question has been raised whether J_1\J_2 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

Keywords

Cite

@article{arxiv.1309.6656,
  title  = {A non-laminar dynamical Green current},
  author = {Romain Dujardin},
  journal= {arXiv preprint arXiv:1309.6656},
  year   = {2014}
}

Comments

Some modifications in the proofs of Lemmas 2.7 and 2.8

R2 v1 2026-06-22T01:34:07.618Z