A two-dimensional polynomial mapping with a wandering Fatou component

Matthieu Astorg; Xavier Buff; Romain Dujardin; Han Peters; Jasmin Raissy

doi:10.4007/annals.2016.184.1.2

A two-dimensional polynomial mapping with a wandering Fatou component

Matthieu Astorg
, Xavier Buff
, Romain Dujardin
, Han Peters
, Jasmin Raissy

Université de Toulouse
Université Gustave Eiffel
University of Amsterdam

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

38 Citations (Scopus)

Résumé

We show that there exist polynomial endomorphisms of C², possessing a wandering Fatou component. These mappings are polynomial skewproducts, 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.

langue originale	Anglais
Pages (de - à)	263-313
Nombre de pages	51
journal	Annals of Mathematics
Volume	184
Numéro de publication	1
Les DOIs	https://doi.org/10.4007/annals.2016.184.1.2
état	Publié - 1 juil. 2016
Modification externe	Oui

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10.4007/annals.2016.184.1.2

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title = "A two-dimensional polynomial mapping with a wandering Fatou component",

abstract = "We show that there exist polynomial endomorphisms of C2, possessing a wandering Fatou component. These mappings are polynomial skewproducts, 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.",

author = "Matthieu Astorg and Xavier Buff and Romain Dujardin and Han Peters and Jasmin Raissy",

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AB - We show that there exist polynomial endomorphisms of C2, possessing a wandering Fatou component. These mappings are polynomial skewproducts, 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.

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A two-dimensional polynomial mapping with a wandering Fatou component

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