A two-dimensional polynomial mapping with a wandering Fatou component

We show that there exist polynomial endomorphisms of ℂ2, possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorphically of ℙ2(ℂ). We also find real examples with wandering domains in ℝ2. The proof relies on parabolic implosion techniq...

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Bibliographic Details
Published in:Annals of mathematics 2016-07, Vol.184 (1), p.263-313
Main Authors: Astorg, Matthieu, Buff, Xavier, Dujardin, Romain, Peters, Han, Raissy, Jasmin
Format: Article
Language:English
Subjects:
Complex Variables
Coordinate systems
Critical points
Dynamical Systems
Eggbeaters
Implosions
Integers
Logarithms
Mathematics
Petals
Polynomials
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Summary:We show that there exist polynomial endomorphisms of ℂ2, possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorphically of ℙ2(ℂ). We also find real examples with wandering domains in ℝ2. The proof relies on parabolic implosion techniques and is based on an original idea of M. Lyubich.
ISSN:0003-486X
DOI:10.4007/annals.2016.184.1.2