Hyperbolic components of McMullen maps
Hyperbolic components of McMullen maps
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DOI：
10.24033/asens.2256
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
Weiyuan Qiu;P. Roesch;Xiaoguang Wang;Yongcheng Yin
中科院分区：
文献类型：
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作者：
Weiyuan Qiu;P. Roesch;Xiaoguang Wang;Yongcheng Yin
在本文中，我们研究了麦克马伦映射的双曲分量。我们证明了所有双曲分支的边界都是Jordan曲线。这解决了Devaney提出的一个问题。因此，我们证明了尖点在无界双曲分量的边界上是稠密的。这是一个动力学模拟的McMullen定理，尖点是密集的Bers'边界上的Teichm\“uller空间。
In this article, we study the hyperbolic components of McMullen maps. We show that the boundaries of all hyperbolic components are Jordan curves. This settles a problem posed by Devaney. As a consequence, we show that cusps are dense on the boundary of the unbounded hyperbolic component. This is a dynamical analogue of McMullen's theorem that cusps are dense on the Bers' boundary of Teichm\"uller space.