Fatou-Julia theory for non-uniformly quasiregular maps

TL;DR

This paper extends Fatou-Julia iteration theory to certain non-uniformly quasiregular maps in higher dimensions, broadening the scope beyond uniformly quasiregular maps.

Contribution

It introduces new results for classes of quasiregular maps that are not uniformly quasiregular, expanding the theoretical framework.

Findings

Extended Fatou-Julia theory to non-uniformly quasiregular maps

Identified classes of quasiregular maps with similar dynamical properties

Broadened understanding of higher-dimensional quasiregular dynamics

Abstract

Many results of the Fatou-Julia iteration theory of rational functions extend to uniformly quasiregular maps in higher dimensions. We obtain results of this type for certain classes of quasiregular maps which are not uniformly quasiregular.