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.
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Dedicated to the Memory of Professor Lei Tan
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Chéritat, A., Epstein, A.L. Bounded type Siegel disks of finite type maps with few singular values. Sci. China Math. 61, 2139–2156 (2018). https://doi.org/10.1007/s11425-018-9381-4
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DOI: https://doi.org/10.1007/s11425-018-9381-4