Geodesic
A two-dimensional polynomial mapping with a wandering Fatou component
Matthieu Astorg1 ; Xavier Buff1 ; Romain Dujardin2 ; Han Peters3 ; Jasmin Raissy1
1 Institut de Mathématiques de Toulouse, Université de Toulouse, CNRS, Toulouse, France
2 Laboratoire d'Analyse et de Mathématiques Appliquées, Université Paris-Est Marne-la-Vallée, Champs-sur-Marne, France
3 KdV Institute for Mathematics University of Amsterdam, The Netherlands
Annals of mathematics, Tome 184 (2016) no. 1, pp. 263-313.

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We show that there exist polynomial endomorphisms of $\mathbb{C}^2$, possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorphically of $\mathbb{P}^2(\mathbb{C})$. We also find real examples with wandering domains in $\mathbb{R}^2$. The proof relies on parabolic implosion techniques and is based on an original idea of M. Lyubich.
DOI : 10.4007/annals.2016.184.1.2

Matthieu Astorg 1 ; Xavier Buff 1 ; Romain Dujardin 2 ; Han Peters 3 ; Jasmin Raissy 1

1 Institut de Mathématiques de Toulouse, Université de Toulouse, CNRS, Toulouse, France
2 Laboratoire d'Analyse et de Mathématiques Appliquées, Université Paris-Est Marne-la-Vallée, Champs-sur-Marne, France
3 KdV Institute for Mathematics University of Amsterdam, The Netherlands 
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     title = {A two-dimensional polynomial mapping  with a wandering {Fatou} component},
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Matthieu Astorg; Xavier Buff; Romain Dujardin; Han Peters; Jasmin Raissy. A two-dimensional polynomial mapping  with a wandering Fatou component. Annals of mathematics, Tome 184 (2016) no. 1, pp. 263-313. doi : 10.4007/annals.2016.184.1.2. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.184.1.2/

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