Symmetries for Julia sets of rational maps
Dynamical Systems
2019-05-16 v2
Abstract
Since the 1980s, much progress has been done in completely determining which functions share a Julia set. The polynomial case was completely solved in 1995, and it was shown that the symmetries of the Julia set play a central role in answering this question. The rational case remains open, but it was already shown to be much more complex than the polynomial one. Here, we offer partial extensions to Beardon's results on the symmetry group of Julia sets, and discuss them in the context of singularly perturbed maps.
Keywords
Cite
@article{arxiv.1902.09642,
title = {Symmetries for Julia sets of rational maps},
author = {Gustavo Rodrigues Ferreira},
journal= {arXiv preprint arXiv:1902.09642},
year = {2019}
}
Comments
11 pages, 3 figure. Corrected a mistake in Lemma 2.6 (previously 2.3), added and expanded results on potentials and added figures to Section 3