Benitez Lopez, Tania Gricel
(2022)
Hereditarily indecomposable Julia continua of transcendental entire functions.
PhD thesis, University of Liverpool.
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Abstract
This thesis studies the topology of the Julia set of transcendental entire functions of disjoint type. It is known that the Julia set of such entire functions may contain topological objects which could be considered ``pathological''. In this sense, we may ask how pathological the Julia set could become. Here, we prove the existence of a transcendental entire function of disjoint type for which the connected components of its Julia set together with infinity are pseudo-arcs. Furthermore, the disjoint-type entire function can be chosen to have finite lower order of growth.
| Item Type: | Thesis (PhD) |
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| Divisions: | Faculty of Science and Engineering > School of Physical Sciences |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 16 Dec 2022 15:57 |
| Last Modified: | 18 Jan 2023 19:43 |
| DOI: | 10.17638/03166198 |
| Supervisors: |
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| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3166198 |
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