  We present a perturbative approach to the study of the Hofstadter model for
when the amount of flux per plaquette is close to a rational fraction. Within
this approximation certain eigenstates of the system are shown to be
multi-component wavefunctions that connect smoothly to the Landau levels of the
continuum. The perturbative corrections to these are higher Landau level
contributions that break rotational invariance and allow the perturbed states
to adopt the symmetry of the lattice. In the presence of interactions, this
approach allows for the calculation of generalised Haldane pseudopotentials,
and in turn, the many-body properties of the system. The method is sufficiently
general that it can apply to a wide variety of lattices, interactions and
magnetic field strengths.
