Automorphisms of ℂk with an invariant non-recurrent attracting Fatou component biholomorphic to ℂ x (ℂ*)k-1.

We prove the existence of automorphisms of ℂ^k, k ≥ 2, having an invariant, non-recurrent Fatou component biholomorphic to ℂ x (ℂ*)^k-1 which is attracting, in the sense that all the orbits converge to a fixed point on the boundary of the component. As a corollary, we obtain a Runge copy of ℂ x (ℂ*) ^k-1 in ℂk. The constructed Fatou component also avoids k analytic discs intersecting transversally at the fixed point. [ABSTRACT FROM AUTHOR]