In this work we consider unidimensional dynamical systems, that is, systems generated by iterating a function defined on the real line. The main results we prove is the Sarkovskii theorem (and some applications), that claims that if there is a 3-periodic orbit for some real continuous function f, then f also possesses k-periodic orbits, for every k. We also prove a generalization of this theorem, considering another ordering < in the set of natural numbers and proving that, with this new order