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.