NON-WANDERING FATOU COMPONENTS FOR STRONGLY ATTRACTING POLYNOMIAL SKEW PRODUCTS
Résumé
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 in $\mathbb{C}^2$ 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 fattened Fatou component.
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