NON-WANDERING FATOU COMPONENTS FOR STRONGLY ATTRACTING POLYNOMIAL SKEW PRODUCTS

Zhuchao Ji (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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.

Domaines: Systèmes dynamiques [math.DS]; Variables complexes [math.CV]

Zhuchao Ji. NON-WANDERING FATOU COMPONENTS FOR STRONGLY ATTRACTING POLYNOMIAL SKEW PRODUCTS. 2018. ⟨hal-01710467v1⟩