Iterated monodromy groups of exponential maps

  • Bernhard Reinke

    Aix-Marseille Université, Marseille, France; Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
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Abstract

This paper introduces iterated monodromy groups for transcendental functions and discusses them in the simplest setting, for post-singularly finite exponential functions. These groups are self-similar groups in a natural way, based on an explicit construction in terms of kneading sequences. We investigate the group theoretic properties of these groups, and show in particular that they are amenable, but they are not elementary subexponentially amenable.

Cite this article

Bernhard Reinke, Iterated monodromy groups of exponential maps. Groups Geom. Dyn. 18 (2024), no. 3, pp. 849–867

DOI 10.4171/GGD/777