  We calculate the energy band structure for electrons in an external periodic
potential combined with a perpendicular magnetic field. Electron-electron
interactions are included within a Hartree approximation. The calculated energy
spectra display a considerable degree of self-similarity, just as the
``Hofstadter butterfly.'' However, screening affects the butterfly, most
importantly the bandwidths oscillate with magnetic field in a characteristic
way. We also investigate the dynamic response of the electron system in the
far-infrared (FIR) regime. Some of the peaks in the FIR absorption spectra can
be interpreted mainly in semiclassical terms, while others originate from
inter(sub)band transitions.
