Bondarenko I. Self-similar automorphism groups of homogeneous rooted trees

Thesis is devoted to study of self-similar automorphism groups of homogeneous rooted trees generated by finite bounded automata and iterated monodromy groups of post-critically finite quadratic polynomials. It is proved that groups generated by finite bounded automata are contracting. The contracting groups with post-critically finite limit spaces are described. The nuclei of iterated monodromy groups of post-critically finite quadratic polynomials are described. The methods for construction of Schreier graphs G_n of iterated monodromy groups of sub-hyperbolic quadratic polynomials are given. The structure of these graphs is described. An efficient method is given for finding the orbital contracting coefficient and the growth of diameters of Schreier graphs G_n.