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Non-wandering Fatou Components for Strongly Attracting Polynomial Skew Products

  • Zhuchao JiEmail author
Article
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Abstract

We show a partial generalization of Sullivan’s non-wandering domain theorem in complex dimension two. More precisely, we show the non-existence of wandering Fatou components for polynomial skew products of \( {\mathbb {C}}^2\) with an invariant attracting fiber, under the assumption that the multiplier \( \lambda \) is small. We actually show a stronger result, namely that every forward orbit of any vertical Fatou disk intersects a bulging Fatou component.

Keywords

Polynomial skew product Fatou component Non-wandering domain theorem 

Mathematics Subject Classification

37F10 37F50 32H50 

Notes

Acknowledgements

I would like to thank Romain Dujardin for drawing my attention to the subject and for his invaluable help. The work is partially supported by ANR-LAMBDA, ANR-13-BS01-0002. I also would like to thank the referee for the nice suggestions on the structure of the paper.

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Copyright information

© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.Laboratoire de Probabilités, Statistique et Modélisation (LPSM, UMR 8001)Sorbonne UniversitésParis Cedex 05France

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