The Hausdorff Dimension of Escaping Sets of Meromorphic Functions in the Speiser Class
(2024) In International Mathematics Research Notices 2024(9). p.7281-7306- Abstract
Bergweiler and Kotus gave sharp upper bounds for the Hausdorff dimension of the escaping set of a meromorphic function in the Eremenko–Lyubich class, in terms of the order of the function and the maximal multiplicity of the poles. We show that these bounds are also sharp in the Speiser class. We apply this method also to construct meromorphic functions in the Speiser class with preassigned dimensions of the Julia set and the escaping set.
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https://lup.lub.lu.se/record/2726166c-7bfd-491f-8fd4-4f99c587bfd1
- author
- Bergweiler, Walter and Cui, Weiwei LU
- organization
- publishing date
- 2024-05-01
- type
- Contribution to journal
- publication status
- published
- subject
- in
- International Mathematics Research Notices
- volume
- 2024
- issue
- 9
- pages
- 26 pages
- publisher
- Oxford University Press
- external identifiers
-
- scopus:85193002377
- ISSN
- 1073-7928
- DOI
- 10.1093/imrn/rnad126
- language
- English
- LU publication?
- yes
- id
- 2726166c-7bfd-491f-8fd4-4f99c587bfd1
- date added to LUP
- 2024-05-23 10:24:57
- date last changed
- 2024-05-23 10:26:18
@article{2726166c-7bfd-491f-8fd4-4f99c587bfd1, abstract = {{<p>Bergweiler and Kotus gave sharp upper bounds for the Hausdorff dimension of the escaping set of a meromorphic function in the Eremenko–Lyubich class, in terms of the order of the function and the maximal multiplicity of the poles. We show that these bounds are also sharp in the Speiser class. We apply this method also to construct meromorphic functions in the Speiser class with preassigned dimensions of the Julia set and the escaping set.</p>}}, author = {{Bergweiler, Walter and Cui, Weiwei}}, issn = {{1073-7928}}, language = {{eng}}, month = {{05}}, number = {{9}}, pages = {{7281--7306}}, publisher = {{Oxford University Press}}, series = {{International Mathematics Research Notices}}, title = {{The Hausdorff Dimension of Escaping Sets of Meromorphic Functions in the Speiser Class}}, url = {{http://dx.doi.org/10.1093/imrn/rnad126}}, doi = {{10.1093/imrn/rnad126}}, volume = {{2024}}, year = {{2024}}, }