Hyperbolic components of McMullen maps
  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. 
Weiyuan Qiu, Pascale Roesch, Xiaoguang Wang, Yongcheng Yin
math.DS math.CV