Hyperbolic components of McMullen maps
Dynamical Systems
2012-10-03 v2 Complex Variables
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 Teichm\"uller space.
Cite
@article{arxiv.1207.0266,
title = {Hyperbolic components of McMullen maps},
author = {Weiyuan Qiu and Pascale Roesch and Xiaoguang Wang and Yongcheng Yin},
journal= {arXiv preprint arXiv:1207.0266},
year = {2012}
}
Comments
29 pages, 6 figures. complex dynamical system