Global periodicity and complete integrability of discrete dynamical systems

Consider the discrete dynamical system generated by a map F It is said that it is globally periodic if there exists a natural number p such that F-p(x) =x for all x in the phase space. On the other hand, it is called completely integrable if it has as many functionally independent first integrals as the dimension of the phase space. In this paper, we relate both concepts. We also give a large list of globally periodic dynamical systems together with a complete set of their first integrals, emphasizing the ones coming from difference equations.