Polynomial shift--like maps in ${\mathbb{C}}^k$

Abstract

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.

There is a considerable change in the results in addition to the change in title