Iterated Monodromy Groups of Entire Maps and Dendroid Automata
Dynamical Systems
2022-10-20 v1 Group Theory
Abstract
This paper discusses iterated monodromy groups for transcendental functions. We show that for every post-singularly finite entire transcendental function, the iterated monodromy action can be described by bounded activity automata of a special form, called "dendroid automata". In particular, we conclude that the iterated monodromy group of a post-singularly finite entire function is amenable if and only if the monodromy group is.
Keywords
Cite
@article{arxiv.2210.10385,
title = {Iterated Monodromy Groups of Entire Maps and Dendroid Automata},
author = {Bernhard Reinke},
journal= {arXiv preprint arXiv:2210.10385},
year = {2022}
}