Article Dans Une Revue Science China Mathematics Année : 2018

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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Dates et versions

hal-01964476 , version 1 (13-10-2021)

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Arnaud Chéritat, Adam Lawrence L Epstein. Bounded type Siegel disks of finite type maps with few singular values. Science China Mathematics, 2018, 61 (12), pp.2139-2156. ⟨10.1007/s11425-018-9381-4⟩. ⟨hal-01964476⟩
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