Morozov D. Finite state conjugation of linear izometric functions on the metric space of 2-adic numbers

The dissertation is devoted to the study the problem of finite state conjugation for automorphisms of maximal pro-oder of an infinity binary rooted tree which are realized as linear functions on the ring of integer 2-adic numbers. Automorphisms of the one rooted infinite binary tree (the degree of all vertices except the root one equals 3) can be identified with bijections of the ring of integer 2-adic numbers. For instance, so called the adding machine can be defined as the function. The centralizer is a closure of the cyclic group in the topology of projective limit. The main resault is the theorem : two finite state automorphisms of maximal pro- order ax+b and cx+d which are linear functions are conjugate in FAutT2 if and only if a=b.