Speiser class Julia sets with dimension near one
Complex Variables
2020-07-17 v1 Dynamical Systems
Abstract
For any we construct an entire function with three singular values whose Julia set has Hausdorff dimension at most . Stallard proved that the dimension must be strictly larger than 1 whenever has a bounded singular set, but no examples with finite singular set and dimension strictly less than 2 were previously known.
Cite
@article{arxiv.2007.07951,
title = {Speiser class Julia sets with dimension near one},
author = {Christopher J. Bishop and Simon Albrecht},
journal= {arXiv preprint arXiv:2007.07951},
year = {2020}
}
Comments
53 pages, 25 figures