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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

Quasiregular mappings of polynomial type in $ \mathbb{R}^{2}$


Authors: Alastair Fletcher and Dan Goodman
Journal: Conform. Geom. Dyn. 14 (2010), 322-336
MSC (2010): Primary 30C65; Secondary 30D05, 37F10, 37F45
Published electronically: November 23, 2010
MathSciNet review: 2738532
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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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Additional Information

Alastair Fletcher
Affiliation: Institute of Mathematics, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: alastair.fletcher@warwick.ac.uk

Dan Goodman
Affiliation: Equipe Audition, Département d’Etudes Cognitives, Ecole Normale Supérieure, 29 Rue d’Ulm 75230, Paris, Cedex 05, France
Email: dan.goodman@ens.fr

DOI: http://dx.doi.org/10.1090/S1088-4173-2010-00219-5
PII: S 1088-4173(2010)00219-5
Keywords: Quasiregular dynamics
Received by editor(s): June 1, 2010
Published electronically: November 23, 2010
Additional Notes: The first author is supported by EPSRC grant EP/G050120/1.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.