  Neutrinos in a core-collapse supernova undergo coherent flavor
transformations in their own background. We explore this phenomenon during the
cooling stage of the explosion. Our three-flavor calculations reveal
qualitatively new effects compared to a two-flavor analysis. These effects are
especially clearly seen for the inverted mass hierarchy: we find a different
pattern of spectral "swaps" in the neutrino spectrum and a novel "mixed"
spectrum for the antineutrinos. A brief discussion of the relevant physics is
presented, including the instability of the two-flavor evolution trajectory,
the 3-flavor pattern of spectral "swaps," and partial nonadiabaticity of the
evolution.
