A two-dimensional polynomial mapping with a wandering Fatou component
Astorg, Matthieu · Buff, Xavier · Dujardin, Romain · Peters, Han · Raissy, Jasmin
Original · EN
We show that there exist polynomial endomorphisms of C², possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorphically of P²(C). We also find real examples with wandering domains in R². The proof is based on parabolic implosion techniques, and is based on an original idea of M. Lyubich.
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