Quasiregular mappings of polynomial type in ℝ²

Fletcher, Alastair; Goodman, Dan

doi:10.1090/S1088-4173-2010-00219-5

Quasiregular mappings of polynomial type in $\mathbb {R}^{2}$
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by Alastair Fletcher and Dan Goodman

Conform. Geom. Dyn. 14 (2010), 322-336

DOI: https://doi.org/10.1090/S1088-4173-2010-00219-5

Published electronically: November 23, 2010

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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 $\mathbb {R}^{2}$ which are a composition of a quadratic polynomial and an affine stretch.

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