On the growth of iterated monodromy groups

2004/05/24 by Kai-Uwe Bux, Bux, Kai-Uwe, Rodrigo Perez +1 · 1 citation
Mathematics · #20F65 #37F20 #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #math.DS #math.GR #msc:20F65 #msc:37F20

paper · pdf · doi:10.48550/arxiv.math/0405456

15 pages, 1 figure. Revised abstract and introduction

arxiv created 2004/06/02 · arxiv updated 2009/12/01

Abstract

Nekrashevych conjectured that the iterated monodromy groups of quadratic polynomials with preperiodic critical orbit have intermediate growth. We illustrate some of the difficulties that arise in attacking this conjecture and prove subexponential growth for the iterated monodromy group of z²+i. This is the first non-trivial example supporting the conjecture.

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• A just-infinite iterated monodromy group without the congruence subgroup property

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