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The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class

Bergweiler, Walter and Cui, Weiwei LU (2022) In Mathematische Zeitschrift 302(4). p.2193-2205
Abstract

We show that for each d∈ (0 , 2] there exists a meromorphic function f such that the inverse function of f has three singularities and the Julia set of f has Hausdorff dimension d.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Eremenko–Lyubich class, Fatou set, Hausdorff dimension, Julia set, Meromorphic function, Speiser class
in
Mathematische Zeitschrift
volume
302
issue
4
pages
13 pages
publisher
Springer
external identifiers
  • scopus:85138527451
ISSN
0025-5874
DOI
10.1007/s00209-022-03142-0
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2022, The Author(s).
id
a76b0d4b-3ac5-49af-8be0-b216d4846073
date added to LUP
2023-02-04 21:49:19
date last changed
2025-04-04 14:46:01
@article{a76b0d4b-3ac5-49af-8be0-b216d4846073,
  abstract     = {{<p>We show that for each d∈ (0 , 2] there exists a meromorphic function f such that the inverse function of f has three singularities and the Julia set of f has Hausdorff dimension d.</p>}},
  author       = {{Bergweiler, Walter and Cui, Weiwei}},
  issn         = {{0025-5874}},
  keywords     = {{Eremenko–Lyubich class; Fatou set; Hausdorff dimension; Julia set; Meromorphic function; Speiser class}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{2193--2205}},
  publisher    = {{Springer}},
  series       = {{Mathematische Zeitschrift}},
  title        = {{The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class}},
  url          = {{http://dx.doi.org/10.1007/s00209-022-03142-0}},
  doi          = {{10.1007/s00209-022-03142-0}},
  volume       = {{302}},
  year         = {{2022}},
}