It is well-known that the dynamics of the Arnold circle map is phase-locked
in regions of the parameter space called Arnold tongues. If the map is
invertible, the only possible dynamics is either quasiperiodic motion, or
phase-locked behavior with a unique attracting periodic orbit. Under the
influence of quasiperiodic forcing the dynamics of the map changes
dramatically. Inside the Arnold tongues open regions of multistability exist,
and the parameter dependency of the dynamics becomes rather complex. This paper
discusses the bifurcation structure inside the Arnold tongue with zero rotation
number and includes a study of nonsmooth bifurcations that happen for large
nonlinearity in the region with strange nonchaotic attractors.Comment: 25 pages, 22 colored figures in reduced quality, submitted to Int. J.
of Bifurcation and Chaos, a supplementary website
(http://www.mpipks-dresden.mpg.de/eprint/jwiersig/0004003/) is provide