  The purpose of this article is to explore a few properties of polynomial
shift-like automorphisms of $\mathbb{C}^k.$ We first prove that a
$\nu-$shift-like polynomial map (say $S_a$) degenerates essentially to a
polynomial map in $\nu-$dimensions as $a \to 0.$ Secondly, we show that a
shift-like map obtained by perturbing a hyperbolic polynomial (i.e., $S_a$,
where $|a|$ is sufficiently small) has finitely many Fatou components,
consisting of basins of attraction of periodic points and the component at
infinity.
