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arXiv · 1802.05972

Non-wandering Fatou components for strongly attracting polynomial skew products

Zhuchao Ji
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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.

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Zhuchao Ji. 2018-02-16. Non-wandering Fatou components for strongly attracting polynomial skew products. https://doi.org/10.1007/s12220-018-00127-6

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