Non-Autonomous basins of attraction and their boundaries

We study whether the basin of attraction of a sequence of automorphisms of ℂ ^{k is biholomorphic to} ℂ ^{k. In particular, we show that given any sequence of automorphisms with the same attracting fixed point, the basin is biholomorphic to} ℂ ^{k, if every map is iterated sufficiently many times. We also construct Fatou-Bieberbach domains in} ℂ² whose boundaries are four-dimensional.