Dynamics of McMullen maps
Dynamical Systems
2012-04-10 v1
Abstract
In this article, we develop the Yoccoz puzzle technique to study a family of rational maps termed McMullen maps. We show that the boundary of the immediate basin of infinity is always a Jordan curve if it is connected. This gives a positive answer to a question of Devaney. Higher regularity of this boundary is obtained in almost all cases. We show that the boundary is a quasi-circle if it contains neither a parabolic point nor a recurrent critical point. For the whole Julia set, we show that the McMullen maps have locally connected Julia sets except in some special cases.
Keywords
Cite
@article{arxiv.1204.1907,
title = {Dynamics of McMullen maps},
author = {Weiyuan Qiu and Xiaoguang Wang and Yongcheng Yin},
journal= {arXiv preprint arXiv:1204.1907},
year = {2012}
}
Comments
Complex dynamics, 51 pages, 13 figures