arXiv:2302.09827 Abstract | arXiv Analytics

arXiv:2302.09827 [math.DS]Abstract References Reviews Resources

The Sullivan dictionary and Bowen-Series maps

Published 2023-02-20Version 1

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.

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

Categories: math.DS, math.CV, math.GT

Subjects: 37F10, 37F32, 30F60, 37D25, 30C62, 30D05, 30F40, 30J10, 37F31, 57M50

Keywords: sullivan dictionary, bowen-series maps, kleinian groups, rational dynamics, expository account

Tags: expository article

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