  In the early Universe, as well as in supernovae and merging neutron stars,
neutrinos have such high densities that they affect each other and exhibit
collective flavor oscillations. A crucial ingredient for fast collective flavor
oscillations is that the electron lepton number (ELN) distribution changes its
sign as a function of direction, i.e., has a zero crossing. We present a study
in two dimensions and show how fast flavor oscillations depend on the ELN and
its crossings. We show that a large number of crossings can inhibit flavor
oscillations. This may be a natural self-limiting mechanism that stabilizes the
flavor content of the dense neutrino gas in a vast majority of scenarios,
especially the early Universe, where the angular distributions for all flavors
are very similar and crossings occur mainly due to fluctuations.
