  We study dynamical systems defined on the combinatorial model of the real
line. We prove that using single-valued maps there are no periodic points of
period 3, which contrasts with the classical and less restrictive setting.
Then, we use Vietoris-like multivalued maps to show that there is more
flexibility, at least in terms of periods, in this combinatorial framework than
in the usual one because we do not have the conditions about the existence of
periods given by the Sharkovski Theorem.
