  Collective neutrino oscillations play a crucial role in transporting lepton
flavor in astrophysical settings like supernovae and neutron star binary merger
remnants, which are characterized by large neutrino densities. In these
settings, simulations in the mean-field approximation show that
neutrino-neutrino interactions can overtake vacuum oscillations and give rise
to fast collective flavor evolution on time-scales $t\propto\mu^{-1}$, with
$\mu$ proportional to the local neutrino density. In this work, we study the
full out-of-equilibrium flavor dynamics in simple multi-angle geometries
displaying fast oscillations in the mean field linear stability analysis.
Focusing on simple initial conditions, we analyze the production of pair
correlations and entanglement in the complete many-body-dynamics as a function
of the number $N$ of neutrinos in the system, for up to thousands of neutrinos.
Similarly to simpler geometries with only two neutrino beams, we identify three
regimes: stable configurations with vanishing flavor oscillations, marginally
unstable configurations with evolution occurring on long time scales
$\tau\approx\mu^{-1}\sqrt{N}$, and unstable configurations showing flavor
evolution on short time scales $\tau\approx\mu^{-1}\log(N)$. We present
evidence that these fast collective modes are generated by the same dynamical
phase transition which leads to the slow bipolar oscillations, establishing a
connection between these two phenomena and explaining the difference in their
time scales. We conclude by discussing a semi-classical approximation which
reproduces the entanglement entropy at short to medium time scales and can be
potentially useful in situations with more complicated geometries where
classical simulation methods starts to become inefficient.
