The Library
Dynamics of degree two quasiregular mappings of the plane of constant dilatation
Tools
Fryer, Robert Neil (2012) Dynamics of degree two quasiregular mappings of the plane of constant dilatation. PhD thesis, University of Warwick.
|
Text
WRAP_THESIS_Fryer_2012.pdf - Submitted Version Download (1990Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b2623469~S1
Abstract
Let h : C ! C be an R-linear map. In this thesis, we explore the dynamics of the quasiregular
mapping h(z)2 + c.
It is well-known that a polynomial can be conjugated by a holomorphic map to w 7! wd
in a neighbourhood of infinity. This map is called a Böttcher coordinate for f near infinity. We
construct a Böttcher type coordinate for compositions of h and polynomials, a class of mappings
first studied in [19]. As an application, we prove that if h is affne and c 2 C, then h(z)2 + c is
not uniformly quasiregular. Via the Böttcher type coordinate, we are able to obtain results for
any degree two mapping of the plane with constant complex dilatation.
We show that any such mapping has either one, two or three fixed external rays, that all
cases can occur, and exhibit how the dynamics changes in each case. We use results from complex
dynamics to prove that these mappings are nowhere uniformly quasiregular in a neighbourhood
of infinity. Finally, we show that in most cases, two such mappings are not quasiconformally
conjugate on a neighbourhood of infinity.
Item Type: | Thesis (PhD) | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Quasiconformal mappings, Functions (Mathematics), Mappings (Mathematics) | ||||
Official Date: | October 2012 | ||||
Dates: |
|
||||
Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Fletcher, A. (Alastair) | ||||
Sponsors: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Extent: | ix, 125 leaves : illustrations | ||||
Language: | eng |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year