On the growth of iterated monodromy groups

Kai-Uwe Bux, Rodrigo Perez

Published 2004-05-24, updated 2004-06-02Version 2

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 $z^2+i$. This is the first non-trivial example supporting the conjecture.