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arXiv · 1207.0266

Hyperbolic components of McMullen maps

Weiyuan Qiu·Pascale Roesch·Xiaoguang Wang·Yongcheng Yin
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Abstract

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 Teichmüller space.

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Weiyuan Qiu, Pascale Roesch, Xiaoguang Wang, Yongcheng Yin. 2012-10-02. Hyperbolic components of McMullen maps. https://arxiv.org/abs/1207.0266

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