Hausdorff dimension of escaping sets of meromorphic functions II
(2023) In Ergodic Theory and Dynamical Systems 43(5). p.1471-1491- Abstract
A function which is transcendental and meromorphic in the plane has at least two singular values. On the one hand, if a meromorphic function has exactly two singular values, it is known that the Hausdorff dimension of the escaping set can only be either <![CDATA[ $2$ ]]> or <![CDATA[ $1/2$ ]]>. On the other hand, the Hausdorff dimension of escaping sets of Speiser functions can attain every number in <![CDATA[ $[0,2]$ ]]> (cf. [M. Aspenberg and W. Cui. Hausdorff dimension of escaping sets of meromorphic functions. Trans. Amer. Math. Soc. 374(9) (2021), 6145-6178]). In this paper, we show that number of singular values which is needed to attain every Hausdorff dimension of escaping sets is not more than <![CDATA[ $4$... (More)
A function which is transcendental and meromorphic in the plane has at least two singular values. On the one hand, if a meromorphic function has exactly two singular values, it is known that the Hausdorff dimension of the escaping set can only be either <![CDATA[ $2$ ]]> or <![CDATA[ $1/2$ ]]>. On the other hand, the Hausdorff dimension of escaping sets of Speiser functions can attain every number in <![CDATA[ $[0,2]$ ]]> (cf. [M. Aspenberg and W. Cui. Hausdorff dimension of escaping sets of meromorphic functions. Trans. Amer. Math. Soc. 374(9) (2021), 6145-6178]). In this paper, we show that number of singular values which is needed to attain every Hausdorff dimension of escaping sets is not more than <![CDATA[ $4$ ]]>.
(Less)
- author
- Aspenberg, Magnus LU and Cui, Weiwei LU
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- escaping sets, meromorphic functions, quasiconformal surgery, singular values, Speiser functions
- in
- Ergodic Theory and Dynamical Systems
- volume
- 43
- issue
- 5
- pages
- 1471 - 1491
- publisher
- Cambridge University Press
- external identifiers
-
- scopus:85124914323
- ISSN
- 0143-3857
- DOI
- 10.1017/etds.2022.5
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © The Author(s), 2022. Published by Cambridge University Press.
- id
- 4b38ee14-b77c-46b0-a927-dd536a74745e
- date added to LUP
- 2022-04-12 16:16:46
- date last changed
- 2023-10-26 14:58:51
@article{4b38ee14-b77c-46b0-a927-dd536a74745e, abstract = {{<p>A function which is transcendental and meromorphic in the plane has at least two singular values. On the one hand, if a meromorphic function has exactly two singular values, it is known that the Hausdorff dimension of the escaping set can only be either <![CDATA[ $2$ ]]> or <![CDATA[ $1/2$ ]]>. On the other hand, the Hausdorff dimension of escaping sets of Speiser functions can attain every number in <![CDATA[ $[0,2]$ ]]> (cf. [M. Aspenberg and W. Cui. Hausdorff dimension of escaping sets of meromorphic functions. Trans. Amer. Math. Soc. 374(9) (2021), 6145-6178]). In this paper, we show that number of singular values which is needed to attain every Hausdorff dimension of escaping sets is not more than <![CDATA[ $4$ ]]>. </p>}}, author = {{Aspenberg, Magnus and Cui, Weiwei}}, issn = {{0143-3857}}, keywords = {{escaping sets; meromorphic functions; quasiconformal surgery; singular values; Speiser functions}}, language = {{eng}}, number = {{5}}, pages = {{1471--1491}}, publisher = {{Cambridge University Press}}, series = {{Ergodic Theory and Dynamical Systems}}, title = {{Hausdorff dimension of escaping sets of meromorphic functions II}}, url = {{http://dx.doi.org/10.1017/etds.2022.5}}, doi = {{10.1017/etds.2022.5}}, volume = {{43}}, year = {{2023}}, }