A two-dimensional polynomial mapping with a wandering Fatou component
  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. 
Matthieu Astorg, Xavier Buff, Romain Dujardin, Han Peters, Jasmin   Raissy
math.DS math.CV