Analogs of Essential Singularities for Sequences of Polynomial Mappings

Abstract

For a sequence of polynomial self-mappings of $\mathbb{C}^\user1{n}$ and a given ball in $\mathbb{C}^\user1{n}$, we state conditions guaranteeing that the union of images of any larger concentric ball is everywhere dense. Under slightly more severe conditions, one can use a sequence of concentric balls (one for each mapping) with radii tending to zero. The common center of these balls is, in a sense, an essential singularity of the sequence of mappings.