Analogs of Essential Singularities for Sequences of Polynomial Mappings

I. M. Dektyarev

Vladimir State Pedagogical University

Abstract: For a sequence of polynomial self-mappings of $\mathbb{C}^n$ and a given ball in $\mathbb{C}^n$, 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.

UDC: 515.16

Received: 29.05.2000

DOI: 10.4213/faa270

 English version: Functional Analysis and Its Applications, 2001, 35:4, 261–264

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