A polynomial automorphism with a wandering Fatou component

Abstract We construct polynomial automorphisms with wandering Fatou components. The four-dimensional automorphisms H lie in a one-parameter family, depending on the parameter δ ∈ C ∖ { 0 } , and as δ → 0 the automorphisms degenerate to the two-dimensional polynomial map P constructed in [2] . Our main result states that if P has a wandering domain, then H does too for δ sufficiently small.