We will talk about a class of groups defined by branched coverings (for instance by polynomial mappings of the complex plane). These group are acting on regular rooted tree in a self-similar way and are often generated by finite automata. We will show how the Julia set of a polynomial can be reconstructed from its iterated monodromy group.
Sponsored in part by the FCT approved projects POCTI 32817/99 and POCTI/MAT/37670/2001 in participation with the European Community Fund FEDER and by FCT through Centro de Matemática da Universidade do Porto. Also sponsored in part by FCT, the Faculdade de Ciências da Universidade do Porto, Programa Operacional Ciência, Tecnologia, Inovação do Quadro Comunitário de Apoio III, and by Caixa Geral de Depósitos.