Hyperbolic components of McMullen maps

@article{Qiu2012HyperbolicCO,
  title={Hyperbolic components of McMullen maps},
  author={Weiyuan Qiu and Pascale Roesch and Xiaoguang Wang and Yongcheng Yin},
  journal={arXiv: Dynamical Systems},
  year={2012}
}
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. 

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