摘要：The most general definition of a dynamical system unifies different areas in mathematics such as continuous differential systems (as ordinary differential equations) and discret dynamical systems (as the iteration of maps). In the first area the time varies continuously, and in the second the time can be measured by integers, i.e. discreetly.

The objective of this talk is to do a brief introduction to the discret dynamical systems of dimension one. Puting special attention to the periodic orbits of the continous self-maps of a closed interval into itself, or of a circle into itself. And mentioning some of the extensions of these results to continuous self-maps of some compact manifolds.