Automata, Dynamical Systems, and Groups

This paper is devoted to the groups of finite automata and their applications in algebra, dynamical systems, and geometry. The groups of synchronous automata as well as the groups of asynchronous automata are considered. The problems of reduction of finite asynchronous automata, the types of growth of finite synchronous automata, and the conditions of embeddability of groups in the group of automata are studied. The automorphism groups of cellular automata are investigated. A group of rational homeomorphisms of the Cantor set is introduced. The dynamics, on the boundary of a tree, determined by an automaton group is investigated. Certain unsolved problems are formulated.