A two-dimensional polynomial mapping with a wandering Fatou component

Abstract

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