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

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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 > 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:	Date Event December 2018 Published 20 November 2018 Available 17 July 2018 Accepted
Date of first compliant deposit:	31 January 2019
Volume:	61
Number:	12
Page Range:	pp. 2139-2156
DOI:	10.1007/s11425-018-9381-4
Status:	Peer Reviewed
Publication Status:	Published
Publisher Statement:	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
Related URLs:	Publisher

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