Abstract
We show that there exist polynomial endomorphisms of $\mathbb{C}^2$, possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorphically of $\mathbb{P}^2(\mathbb{C})$. We also find real examples with wandering domains in $\mathbb{R}^2$. The proof relies on parabolic implosion techniques and is based on an original idea of M. Lyubich.
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