An analogue of Green's Functions for Quasiregular Maps

Autor:	Broderius, Mark, Fletcher, Alastair
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems Mathematics - Complex Variables
Druh dokumentu:	Working Paper
Popis:	Green's functions are highly useful in analyzing the dynamical behavior of polynomials in their escaping set. The aim of this paper is to construct an analogue of Green's functions for planar quasiregular mappings of degree two and constant complex dilatation. These Green's functions are dynamically natural, in that they semi-conjugate our quasiregular mappings to the real squaring map. However, they do not share the same regularity properties as Green's functions of polynomials. We use these Green's functions to investigate properties of the boundary of the escaping set and give several examples to illustrate behavior that does not occur for the dynamics of quadratic polynomials. Comment: 23 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.11256 Zobrazit plný text záznamu View this record from Arxiv