Cantor Julia sets with Hausdorff dimension two
Dynamical Systems
2018-02-06 v1 Complex Variables
Abstract
We prove the existence of Cantor Julia sets with Hausdorff dimension two. In particular, such examples can be found in cubic polynomials. The proof is based on the characterization of the parameter spaces and dynamical planes of cubic polynomials by Branner-Hubbard, and the parabolic bifurcation theory developed by Shishikura in 1990s.
Keywords
Cite
@article{arxiv.1802.01063,
title = {Cantor Julia sets with Hausdorff dimension two},
author = {Fei Yang},
journal= {arXiv preprint arXiv:1802.01063},
year = {2018}
}