A non-laminar dynamical Green current

2013/09/25 by Dujardin, Romain
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.6656

Abstract

A holomorphic endomorphism f of CP² admits a Julia set J₁, defined as usual to be the locus of non-normality of its iterates, 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

Related

• Fatou directions along the Julia set for endomorphisms of CP^k
• Hyperbolic saddle measures and laminarity for holomorphic endomorphisms of P²C
• Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k)
• Equidistribution speed towards the Green current for endomorphisms of P^k
• An a priori bound of endomorphisms of ℂℙ^k and a remark on the Makienko conjecture in dimension one