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 ($\mathtt{\text{pdynamics}}$ and $\mathtt{\text{poincare}}$, respectively), along with the set of scripts \KeTCindy\ for obtaining the \LaTeX\ code corresponding to graphical representations of Poincar'e sections, including animation movies.