Rational maps whose Julia sets are Cantor circles
Dynamical Systems
2019-02-20 v2
Abstract
In this paper, we give a family of rational maps whose Julia sets are Cantor circles and show that every rational map whose Julia set is a Cantor set of circles must be topologically conjugate to one map in this family on their corresponding Julia sets. In particular, we give the specific expressions of some rational maps whose Julia sets are Cantor circles, but they are not topologically conjugate to any McMullen maps on their Julia sets. Moreover, some non-hyperbolic rational maps whose Julia sets are Cantor circles are also constructed.
Keywords
Cite
@article{arxiv.1301.2692,
title = {Rational maps whose Julia sets are Cantor circles},
author = {Weiyuan Qiu and Fei Yang and Yongcheng Yin},
journal= {arXiv preprint arXiv:1301.2692},
year = {2019}
}
Comments
28 pages, 6 figures; To appear in Ergod. Th. & Dynam. Sys