A criterion to generate carpet Julia sets
Dynamical Systems
2017-08-22 v1 Complex Variables
Abstract
It was known that the Sierpi\'{n}ski carpets can appear as the Julia sets in the families of some rational maps. In this article we present a criterion that guarantees the existence of the carpet Julia sets in some rational maps having exactly one fixed (super-) attracting or parabolic basin. We show that this criterion can be applied to some well known rational maps, such as McMullen maps and Morosawa-Pilgrim family. Moreover, we give also some special examples whose Julia sets are Sierpi\'{n}ski carpets.
Keywords
Cite
@article{arxiv.1708.05848,
title = {A criterion to generate carpet Julia sets},
author = {Fei Yang},
journal= {arXiv preprint arXiv:1708.05848},
year = {2017}
}
Comments
12 pages, 3 figures