  We study the critical points of the black hole scalar potential $V_{BH}$ in
N=2, d=4 supergravity coupled to $n_{V}$ vector multiplets, in an
asymptotically flat extremal black hole background described by a
2(n_{V}+1)-dimensional dyonic charge vector and (complex) scalar fields which
are coordinates of a special K\"{a}hler manifold.
  For the case of homogeneous symmetric spaces, we find three general classes
of regular attractor solutions with non-vanishing Bekenstein-Hawking entropy.
They correspond to three (inequivalent) classes of orbits of the charge vector,
which is in a 2(n_{V}+1)-dimensional representation $R_{V}$ of the U-duality
group. Such orbits are non-degenerate, namely they have non-vanishing quartic
invariant (for rank-3 spaces). Other than the 1/2-BPS one, there are two other
distinct non-BPS classes of charge orbits, one of which has vanishing central
charge.
  The three species of solutions to the N=2 extremal black hole attractor
equations give rise to different mass spectra of the scalar fluctuations, whose
pattern can be inferred by using invariance properties of the critical points
of $V_{BH}$ and some group theoretical considerations on homogeneous symmetric
special K\"{a}hler geometry.
