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Bounded type Siegel disks of finite type maps with few singular values

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Cheritat, Arnaud and Epstein, Adam L. (2018) Bounded type Siegel disks of finite type maps with few singular values. Science China Mathematics, 61 (12). pp. 2139-2156. doi:10.1007/s11425-018-9381-4 ISSN 1674-7283.

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Official URL: https://doi.org/10.1007/s11425-018-9381-4

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Abstract

Let U be an open subset of the Riemann sphere C^ . We give sufficient conditions for which a finite type map f: U → C^ with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-Świątek. We also give sufficient conditions for which, instead, Δ has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-Świątek.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Mappings (Mathematics), Riemann surfaces
Journal or Publication Title: Science China Mathematics
Publisher: Zhongguo Kexue Zazhishe
ISSN: 1674-7283
Official Date: December 2018
Dates:
DateEvent
December 2018Published
20 November 2018Available
17 July 2018Accepted
Volume: 61
Number: 12
Page Range: pp. 2139-2156
DOI: 10.1007/s11425-018-9381-4
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): This is a post-peer-review, pre-copyedit version of an article published in Science China Mathematics. The final authenticated version is available online at: https://doi.org/10.1007/s11425-018-9381-4
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 31 January 2019
Date of first compliant Open Access: 20 November 2019
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