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arXiv · 2210.10385

Iterated Monodromy Groups of Entire Maps and Dendroid Automata

Bernhard Reinke
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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.

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Bernhard Reinke. 2022-10-19. Iterated Monodromy Groups of Entire Maps and Dendroid Automata. https://arxiv.org/abs/2210.10385

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