Automorphisms of C-k 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 C-k. The constructed Fatou component also avoids k analytic discs intersecting transversally at the fixed point.