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

Research output: Contribution to journal › Article › peer-review

38 Citations (Scopus)

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.

Original language	English
Pages (from-to)	263-313
Number of pages	51
Journal	Annals of Mathematics
Volume	184
Issue number	1
DOIs	https://doi.org/10.4007/annals.2016.184.1.2
Publication status	Published - 1 Jul 2016
Externally published	Yes

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10.4007/annals.2016.184.1.2

Cite this

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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.",

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AU - Peters, Han

AU - Raissy, Jasmin

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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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