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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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | 575 | ||||
Number: | No.CONM/575 | ||||
Number of Pages: | 24 | ||||
DOI: | 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 | ||||
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