  We recall results concerning one-dimensional classical and quantum systems
with ladder operators. We obtain the most general one-dimensional classical
systems respectively with a third and a fourth order ladder operators
satisfying polynomial Heisenberg algebras. These systems are written in terms
of the solutions of quartic and quintic equations. We use these results to
present two new families of superintegrable systems and examples of
trajectories that are deformed Lissajous's figures.
