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Science China Mathematics

, Volume 61, Issue 12, pp 2139–2156 | Cite as

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

  • Arnaud ChéritatEmail author
  • Adam Lawrence Epstein
Articles
  • 21 Downloads

Abstract

Let U be an open subset of the Riemann sphere \(\hat {\mathbb{C}}\). We give sufficient conditions for which a finite type map f: U\(\hat {\mathbb{C}}\) 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.

Keywords

Siegel disks quasicircles quasiconformal surgery Schwarzian derivative 

MSC(2010)

37F30 37F40 37F50 

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Copyright information

© Science in China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CNRS, Institut de Mathématiques de ToulouseUniversité Paul SabatierToulouseFrance
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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