Type
Text
Type
Dissertation
Advisor
Lyubich, Mikhail | Bishop, Christopher J. | Sullivan, Dennis | Merenkov, Sergiy.
Date
2017-08-01
Keywords
Mathematics | Complex Analysis | Complex Dynamics | Quasiconformal mappings
Department
Department of Mathematics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree
Identifier
http://hdl.handle.net/11401/78158
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
We use a theorem of Bishop to construct several functions in the Eremenko-Lyubich class $\mathcal{B}$. First it is verified, that in Bishop's initial construction of a wandering domain in $\mathcal{B}$, all wandering Fatou components must be bounded. Next we modify this construction to produce a function in $\mathcal{B}$ with wandering domain and uncountable singular set. Finally we construct a function in $\mathcal{B}$ with unbounded wandering Fatou components. It is shown that these constructions answer two questions posed by Osborne and Sixsmith. | 48 pages
Recommended Citation
Lazebnik, Kirill, "Several Constructions in the Eremenko-Lyubich Class" (2017). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 3653.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/3653