Publication Date

2020

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 studies an interplay between the dynamics of iterated quasiregular map-

pings and certain topological structures. In particular, the relationship between the Julia set

of a uniformly quasiregular mapping f : R 3 → R 3 and the fast escaping set of its associated

Poincaré linearizer is explored. It is shown that, if the former is a Cantor set, then the latter

is a spider’s web. A new class of uniformly quasiregular maps is constructed to which this

result applies. Toward this, a geometrically self-similar Cantor set of genus 2 is constructed.

It is also shown that for any uniformly quasiregular mapping f : R n → R n , n ≥ 2, if the

Julia set of f is a Cantor set, then the Julia set is the closure of the set of repelling periodic

points of f . Some growth estimates on generalized derivatives are established, as well as a

bound on the order of growth of the associated Poincaré linearizer.

Extent

154 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

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