Bounded type Siegel disks of finite type maps with few singular values
Résumé
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, ∆ has not compact closure in U. The main tool is the Schwarzian derivative and area inequalitiesà la Graczyk-Świątek.
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