Quasiregular dynamics on the n-sphere

TL;DR

This paper studies the boundary of escaping sets for quasiregular mappings on R^n, showing it coincides with the Julia set when defined, and shares similar properties even when not defined.

Contribution

It establishes the relationship between the boundary of escaping sets and Julia sets for quasiregular mappings in higher dimensions.

Findings

Boundary of I(f) equals J(f) when J(f) is defined

Boundary of I(f) shares properties with J(f) when J(f) is not defined

Results extend complex dynamics concepts to higher dimensions

Abstract

In this article, we investigate the boundary of the escaping set I(f) for quasiregular mappings on R^n, both in the uniformly quasiregular case and in the polynomial type case. The aim is to show that the boundary of I(f) is the Julia set J(f) when the latter is defined, and shares properties with the Julia set when J(f) is not defined.