Iterated Monodromy Groups of Exponential Maps

2020/04/27 by Bernhard Reinke, Reinke, Bernhard
Mathematics · #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2004.12653

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.

Related

• Iterated Monodromy Groups of Entire Maps and Dendroid Automata
• Iterated Monodromy Groups of Intermediate Growth
• Introduction to Iterated Monodromy Groups
• Iterated monodromy groups of Chebyshev-like maps on ℂⁿ
• Profinite iterated monodromy groups arising from quadratic morphisms with infinite postcritical orbits