Flavor oscillation modes in dense neutrino media

We study two-flavor neutrino oscillations in homogeneous neutrino gases in which neutrinos and antineutrinos are in nearly pure weak interaction states initially. We find that the monopole and dipole oscillation modes can trigger flavor instabilities in the opposite neutrino mass hierarchies in a nearly isotropic neutrino gas. For a class of simple neutrino systems we are able to identify the normal modes of neutrino oscillations in the linear regime. Our results provide new insights into the recently discovered multiazimuthal angle instability of neutrino oscillations in supernovae.