Affiliation:
1. Institute de Mathématiques de Marseille UMR 7373 Aix‐Marseille Université and CRNS 163 Avenue de Luminy Case 901 Marseille 13009 France
Abstract
AbstractWe study the action of groups generated by bounded activity automata with infinite alphabets on their orbital Schreier graphs. We introduce an amenability criterion for such groups based on the recurrence of the first‐level action. This criterion is a natural extension of the result that all groups generated by bounded activity automata with finite alphabets are amenable. Our motivation comes from the investigation of iterated monodromy groups of entire transcendental functions in holomorphic dynamics.
Funder
European Research Council