## Automorphisms of C^2 with an invariant Fatou component biholomorphic to C x C^*.

I will present the construction of a family of automorphisms of **C**^2 having an invariant, non-recurrent Fatou component biholomorphic to **C **x** C*** and which is attracting, in the sense that all the orbits converge to a fixed point on the boundary of the component. (This is a joint work with Filippo Bracci and Berit Stensones).