关于Sine族的David型Siegel矩阵
On David type Siegel Disks of the Sine family
摘要：
2008年，Petersen提出了一系列关于Zakeri和他自己开发的trans-quasiconformal Siegel手术的应用问题。在本文中，我们扩展了Petersen-Zakeri的思想，使手术可以适用于所有的前模型，没有“自由临界点“。我们解释了如何使用这个想法来解决彼得森提出的三个问题。为了详细介绍这一思想，我们着重解决了其中一个问题：我们证明了对于典型的旋转数$0< θ< 1$，$f_θ(z) = e^{2 πi θ} \sin (z)$的Siegel圆盘的边界是一条恰好通过两个临界点$π/2$和$-π/2$的Jordan曲线.
英文摘要：
In 2008 Petersen posed a list of questions on the application of trans-quasiconformal Siegel surgery developed by Zakeri and himself. In this paper we extend Petersen-Zakeri's idea so that the surgery can be applied to all the premodels which have no "free critical points". We explain how the idea is used in solving three of the questions posed by Petersen. To present the details of the idea, we focus on the solution of one of them: we prove that for typical rotation numbers $0< θ< 1$, the boundary of the Siegel disk of $f_θ(z) = e^{2 πi θ} \sin (z)$ is a Jordan curve which passes through exactly two critical points $π/2$ and $-π/2$.
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