A complete description of the iterated monodromy groups of postcritically finite backward polynomial iterations is given in terms of their actions on rooted trees and automata generating them. Weâ€¦ (More)

Since 1929 when von Neumann [vN29] introduced the notion of an invariant mean on a group (and more generally on a G-set) there is a permanent interest in the study of the phenomenon known asâ€¦ (More)

We show that if a group G acting faithfully on a rooted tree T has a free subgroup, then either there exists a point w of the boundary âˆ‚T and a free subgroup of G with trivial stabilizer of w, orâ€¦ (More)

For every infinite sequence Ï‰ = x1x2 . . ., with xi âˆˆ {0, 1}, we construct an infinite 4-regular graph XÏ‰. These graphs are precisely the Schreier graphs of the action of a certain self-similar groupâ€¦ (More)

Self-similar group actions (or self-similar groups) have proved to be interesting mathematical objects from the point of view of group theory and from the point of view of many other fields ofâ€¦ (More)

We associate a group IMG(f) to every covering f of a topological space M by its open subset. It is the quotient of the fundamental group Ï€1(M) by the intersection of the kernels of its monodromyâ€¦ (More)

This is an overview of results concerning applications of self-similar groups generated by automata to fractal geometry and dynamical systems. Few proofs are given, interested reader can find theâ€¦ (More)