INFINITE PERIODIC POINTS OF ENDOMORPHISMS OVER SPECIAL CONFLUENT REWRITING SYSTEMS

We consider endomorphisms of a monoid defined by a special confluent rewriting system that admit a continuous extension to the completion given by reduced infinite words, and study from a dynamical viewpoint the nature of their infinite periodic points. For prefix-convergent endomorphisms and expanding endomorphisms, we determine the structure of the set; of all infinite periodic points in terms of adherence values, bound the periods and show that all regular periodic points are attractors.