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Siegel Disks of the Tangent Family

Cui, Weiwei LU and Nie, Hongming (2021) In Annales Fennici Mathematici 46(1). p.593-600
Abstract

We study Siegel disks in the dynamics of functions from the tangent family. In particular, we prove that a Siegel disk is unbounded if and only if the boundary of its image contains at least one asymptotic value. Moreover, by using quasiconformal surgery we also construct functions in the above family with bounded Siegel disks.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Meromorphic functions, Quasiconformal surgery, Siegel disks, Tangent family
in
Annales Fennici Mathematici
volume
46
issue
1
pages
8 pages
publisher
Finnish Mathematical Society
external identifiers
  • scopus:85130634976
ISSN
2737-0690
DOI
10.5186/aasfm.2021.4635
language
English
LU publication?
yes
additional info
Acknowledgements. The authors thank Weixiao Shen, Gaofei Zhang and Jianhua Zheng for useful discussion and helpful comments. The authors also thank the referees for careful reading and helpful suggestions. The first author was partially supported by the China Postdoctoral Science Foundation (No. 2019M651329). The second author was partially supported by ISF Grant 1226/17. Publisher Copyright: © 2021,Annales Fennici Mathematici,All Rights Reserved
id
de7dfd3a-5dc1-452c-8716-d3107338cba5
date added to LUP
2023-02-04 21:50:55
date last changed
2025-04-04 14:53:39
@article{de7dfd3a-5dc1-452c-8716-d3107338cba5,
  abstract     = {{<p>We study Siegel disks in the dynamics of functions from the tangent family. In particular, we prove that a Siegel disk is unbounded if and only if the boundary of its image contains at least one asymptotic value. Moreover, by using quasiconformal surgery we also construct functions in the above family with bounded Siegel disks.</p>}},
  author       = {{Cui, Weiwei and Nie, Hongming}},
  issn         = {{2737-0690}},
  keywords     = {{Meromorphic functions; Quasiconformal surgery; Siegel disks; Tangent family}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{593--600}},
  publisher    = {{Finnish Mathematical Society}},
  series       = {{Annales Fennici Mathematici}},
  title        = {{Siegel Disks of the Tangent Family}},
  url          = {{http://dx.doi.org/10.5186/aasfm.2021.4635}},
  doi          = {{10.5186/aasfm.2021.4635}},
  volume       = {{46}},
  year         = {{2021}},
}