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NON-WANDERING FATOU COMPONENTS FOR STRONGLY ATTRACTING POLYNOMIAL SKEW PRODUCTS

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.
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https://hal.archives-ouvertes.fr/hal-01710467
Contributor : Zhuchao Ji <>
Submitted on : Tuesday, December 11, 2018 - 11:35:27 AM
Last modification on : Friday, April 10, 2020 - 5:13:34 PM
Document(s) archivé(s) le : Tuesday, March 12, 2019 - 12:47:40 PM

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  • HAL Id : hal-01710467, version 2
  • ARXIV : 1802.05972

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Zhuchao Ji. NON-WANDERING FATOU COMPONENTS FOR STRONGLY ATTRACTING POLYNOMIAL SKEW PRODUCTS. 2018. ⟨hal-01710467v2⟩

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