20E08 3 05C25,43A85 1 2-points homogeneous action,Gelfand pairs 1 20E18 1 20F10 1 20F65 1 37F10 1 43A90 1 Rooted \(q\)-ary tree 1 automata groups 1 branch groups 1 fractal group,labelling 1 group acting on trees 1 iterated monodromy groups 1 profinite grous 1 profinite limits 1 quadratic polynomials 1 rigid vertex stabilizer 1 self-similar groups 1 spherical functions 1 ultrametric space 1