  In this work we provide results on the long time localisation in space
(dynamical localisation) of certain two-dimensional magnetic quantum systems.
The underlying Hamiltonian may have the form $H=H_0+W$, where $H_0$ is
rotationally symmetric, has dense point spectrum, and $W$ is a perturbation
that breaks the rotational symmetry.
  In the latter case, we also give estimates for the growth of the angular
momentum operator in time.
