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A non-laminar Green current

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 (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.
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Submitted on : Thursday, September 25, 2014 - 11:16:20 PM
Last modification on : Thursday, September 29, 2022 - 2:21:15 PM
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  • HAL Id : hal-01068577, version 1


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



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