On the Local Behavior of the Mappings with Non-Bounded Characteristics

TL;DR

This paper investigates the local behavior of generalized space mappings with specific properties, showing that their modulus can grow faster than any logarithmic function near isolated essential singularities.

Contribution

It extends the understanding of differentiable space mappings beyond quasiregular mappings, analyzing their behavior under certain conditions.

Findings

Modulus of mappings can exceed any logarithmic degree near singularities

Mappings with $N$, $N^{-1}$, $ACP$, and $ACP^{-1}$ properties exhibit specific growth behaviors

Results apply to a broader class of mappings than previously studied

Abstract

The present paper is devoted to the study of space mappings, which are more general than quasiregular mappings. The questions of the behavior of differentiable mappings having the so--called $N,$ $N^{-1},$ $ACP$ and $ACP^{-1}$ -- properties are studied in the work. Under some additional conditions, it is showed that the modulus of such mappings $f$ can be more than each degree of logarithmic function at every neighborhood of the isolated essential singularity of $f.$