Publication Date
2021
Document Type
Dissertation/Thesis
First Advisor
Fletcher, Alastair N.
Degree Name
Ph.D. (Doctor of Philosophy)
Legacy Department
Department of Mathematical Sciences
Abstract
This dissertation investigates the role that a new tool called the Zorich transform plays in quasiregular dynamics as a generalization of the logarithmic transform in complex dynamics. In particular we use the Zorich transform to construct analogues of the logarithmic spiral maps and interpolation between radial stretch maps. These constructions are then used to completely classify the orbit space of a quasiregular map. Also, conditions are given in which a quasiregular map $f:D\to\R^n$, where $D\subset\R^n$ is a domain, that is quasiconformal in a neighborhood of a geometrically attracting fixed point can be conjugated by a quasiconformal map to the asymptotic representation of $f$ in a neighborhood of the fixed point. To find such a quasiconformal map, we construct a sequence of quasiconformal maps that converge to the desired map in a neighborhood of the fixed point.
Recommended Citation
Pratscher, Jacob A., "The Zorich Transform and Generalizing Koenigs Linearization Theorem to Quasiregular Maps" (2021). Graduate Research Theses & Dissertations. 7566.
https://huskiecommons.lib.niu.edu/allgraduate-thesesdissertations/7566
Extent
131 pages
Language
eng
Publisher
Northern Illinois University
Rights Statement
In Copyright
Rights Statement 2
NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.
Media Type
Text
