Geodesic
Iterated monodromy groups of exponential maps
Bernhard Reinke1 orcid
1Aix-Marseille Université, Marseille, France; Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Groups, geometry, and dynamics, Tome 18 (2024) no. 3, pp. 849-867

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DOI

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.
DOI : 10.4171/ggd/777
Classification : 37F10, 37B10, 20E08
Mots-clés : iterated monodromy group, transcendental function, exponential function, amenability, Schreier graphs

Bernhard Reinke  1

1 Aix-Marseille Université, Marseille, France; Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany 
Bernhard Reinke. Iterated monodromy groups of exponential maps. Groups, geometry, and dynamics, Tome 18 (2024) no. 3, pp. 849-867. doi: 10.4171/ggd/777
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     title = {Iterated monodromy groups of exponential maps},
     journal = {Groups, geometry, and dynamics},
     pages = {849--867},
     year = {2024},
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     number = {3},
     doi = {10.4171/ggd/777},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/777/}
}
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