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On Böttcher coordinates and quasiregular maps
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Fletcher, Alastair and Fryer, Rob (2012) On Böttcher coordinates and quasiregular maps. In: Jiang, Yunping and Mitra, Sudeb, (eds.) Quasiconformal Mappings, Riemann Surfaces, and Teichmüller Spaces. Contemporary Mathematics, 575 (No.CONM/575). Providence, RI: American Mathematical Society. ISBN 9780821853405
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Official URL: http://dx.doi.org/10.1090/conm/575
Abstract
It is well-known that a polynomial f(z) = adzd(1 + o(1)) can be conjugated by a holomorphic map � to w 7! wd in a neighbourhood of in�nity. This map � is called a Böttcher coordinate for f near in�nity. In this paper we construct a Böttcher type coordinate for compositions of a�ne mappings and polynomials, a class of mappings �rst studied in [9]. As an application, we prove that if h is a�ne and c 2 C, then h(z)2 +c is not uniformly quasiregular.
| Item Type: | Book Item |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Series Name: | Contemporary Mathematics |
| Publisher: | American Mathematical Society |
| Place of Publication: | Providence, RI |
| ISBN: | 9780821853405 |
| ISSN: | 0271-4132 |
| Book Title: | Quasiconformal Mappings, Riemann Surfaces, and Teichmüller Spaces |
| Editor: | Jiang, Yunping and Mitra, Sudeb |
| Date: | 2012 |
| Volume: | 575 |
| Number: | No.CONM/575 |
| Number of Pages: | 24 |
| Identification Number: | 10.1090/conm/575 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Funder: | EPSRC |
| Grant number: | EP/G050120/1 |
| Related URLs: | |
| URI: | http://wrap.warwick.ac.uk/id/eprint/48753 |
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