Hamiltonian systems: symbolical, numerical and graphical study

Hamiltonian dynamical systems can be studied from a variety of viewpoints. Our intention in this paper is to show some examples of usage of two Maxima packages for symbolical and numerical analysis (\texttt{pdynamics} and \texttt{poincare}, respectively), along with the set of scripts \KeTCindy\ for obtaining the \LaTeX\ code corresponding to graphical representations of Poincar\'e sections, including animation movies.