The period set of a map from the Cantor set to itself (Q379452)

The paper under review deals with a classical problem in dynamics: trying to obtain information on the periodic structure of a given discrete dynamical systems. In this case the authors study the problem of continuous self-maps from a cantor set into itself.NEWLINENEWLINEIt is proved that the possible period sets \(P(f)\) are completely unrestricted provided that, in addition, one allows points that are not periodic. However, if every point is periodic, it is showed that a surprising finiteness condition is imposed on the set of all possible periodic points: namely, there is a finite subset \(B\) of \(P(f)\) such that every element of \(P(f)\) is divisible by at least one element of \(B\).