Some Dynamical Properties Of A Cellular Automata On A Countable Group

In this paper,we study some dynamical properties of a cellular automata on a countable group.The main results are as follows:(1)If a cellular automata on a countable group is transi-tive,then it is either sensitive or consist of a single periodic orbit ;(2)By using of the forms of attractor,we give the classification of the cellular automata on a countable group;(3)The set of eventually periodic points of a cellular automata on a countable residually finite group is dense;(4)For a new kind of cellular automata which comes from physical model,we prove that it con-jugates to a cellular automata on a countable group,and then the three results mentioned above hold in this new kind of cellular automata.