The Sullivan dictionary and Bowen-Series maps
Abstract
The Sullivan dictionary between Kleinian groups and rational dynamics describes striking similarities between the fields, both in terms of the objects of study as well as the techniques used. We give an expository account of a recent bridge between the two sides of the dictionary by describing a framework for combining a Fuchsian group with a complex polynomial into a single dynamical system on the Riemann sphere.
Cite
@article{arxiv.2302.09827,
title = {The Sullivan dictionary and Bowen-Series maps},
author = {Mahan Mj and Sabyasachi Mukherjee},
journal= {arXiv preprint arXiv:2302.09827},
year = {2023}
}
Comments
39 pgs, 10 figures. This is an expository paper, partly based on arXiv:2103.00835v1. Some of the examples from arXiv:2103.00835 have now been taken out and moved into the present article. To appear in the 80th birthday volume of Dennis Sullivan, edited by Basmajian, Koberda, Papadopoulos, Seade and Zeinalian, EMS Surveys in Mathematical Sciences