  We consider a disordered two-dimensional system of independent lattice
electrons in a perpendicular magnetic field with rigid confinement in one
direction and generalized periodic boundary conditions (GPBC) in the other
direction. The objects investigated numerically are the orbits in the plane
spanned by the energy eigenvalues and the corresponding center of mass
coordinate in the confined direction, parameterized by the phase characterizing
the GPBC. The Kubo Hall conductivity is expressed in terms of the winding
numbers of these orbits. For vanishing disorder the spectrum of the system
consists of Harper bands with energy levels corresponding to the edge states
within the band gaps. Disorder leads to broadening of the bands. For
sufficiently large systems localized states occur in the band tails. We find
that within the mobility gaps of bulk states the Diophantine equation
determines the value of the Hall conductivity as known for systems with torus
geometry (PBCs in both directions). Within the spectral bands of extended
states the Hall conductivity fluctuates strongly. For sufficiently large
systems the generic behavior of localization-delocalization transitions
characteristic for the quantum Hall effect are recovered.
