Quasiregular mappings of polynomial type in R^2

TL;DR

This paper explores the dynamics of quasiregular mappings in R^2, specifically those formed by composing quadratic polynomials with affine stretches, extending complex dynamics concepts beyond holomorphic functions.

Contribution

It introduces the study of quasiregular mappings of polynomial type in R^2, bridging complex dynamics with quasiregular function theory.

Findings

Characterization of dynamics for quasiregular mappings of polynomial type

Identification of Julia sets for these mappings

Extension of complex dynamics concepts to quasiregular functions

Abstract

Complex dynamics deals with the iteration of holomorphic functions. As is well- known, the first functions to be studied which gave non-trivial dynamics were quadratic polynomials, which produced beautiful computer generated pictures of Julia sets and the Mandelbrot set. In the same spirit, this article aims to study the dynamics of the simplest non-trivial quasiregular mappings. These are mappings in R^2 which are a composition of a quadratic polynomial and an affine stretch.