arXiv:2004.12653 Abstract | arXiv Analytics

arXiv:2004.12653 [math.DS]Abstract References Reviews Resources

Iterated Monodromy Groups of Exponential Maps

Published 2020-04-27Version 1

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.

Comments: 16 Pages, Comments welcome!

Categories: math.DS, math.GR

Subjects: 37F10, 37B10, 20E08

Keywords: iterated monodromy groups, exponential maps, group theoretic properties, post-singularly finite exponential functions, explicit construction

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