The entropies and periods of renewal systems

Abstract

In this work the set of entropies of shifts of finite type is proved to be the same as the set of entropies of renewal systems that are shifts of finite type. The period of a finite set of words is the greatest common divisor of the lengths of the words. We show that the period of a renewal system as a shift space and the minimum of the periods of its generating sets coincide when the system is of finite type or mixing.