Proper polynomial self-maps of the affine space: state of the art and new results

Abstract

Two proper polynomial maps $f_1, \,f_2 \colon \mC^n \lr \mC^n$ are said to be \emph{equivalent} if there exist $Φ_1,\, Φ_2 \in \textrm{Aut}(\mC^n)$ such that $f_2={\Phi }_2\circ f_1\circ {\Phi }_1$. In this article we investigate proper polynomial maps of topological degree $d\ge 2$ up to equivalence. In particular we describe some of our recent results in the case $n=2$ and we partially extend them in higher dimension.

arXiv commentFinal version, as to appear in Contemporary Mathematics, Proceedings of Complex Analysis and Dynamical Systems IV, held in Nahariya, Israel, May 2009.