Infinite-dimensional Thurston theory and transcendental dynamics I: infinite-legged spiders
Volume 261 / 2023
Fundamenta Mathematicae 261 (2023), 157-200
MSC: Primary 37F20; Secondary 37F34, 37F10, 37F12.
DOI: 10.4064/fm82-11-2022
Published online: 26 January 2023
Abstract
We develop techniques that lay out a basis for generalizations of Thurston’s famous Topological Characterization of Rational Functions for an infinite set of marked points and branched coverings of infinite degree. Analogously to the classical theorem we consider Thurston’s $\sigma $-map acting on a Teichmüller space which is this time infinite-dimensional – and this leads to a completely different theory compared to the classical setting.
We demonstrate our techniques by giving an alternative proof of the result by Markus Förster about the classification of exponential functions with the escaping singular value.
