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The Hausdorff Dimension of Escaping Sets of Meromorphic Functions in the Speiser Class

Bergweiler, Walter and Cui, Weiwei LU (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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author
and
organization
publishing date
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}},
}