  Neutrino-neutrino forward scatterings potentially induce collective neutrino
oscillation in dense neutrino gases in astrophysical sites such as
core-collapse supernovae (CCSN) and binary neutron star mergers (BNSM). In this
paper, we present a detailed study of fast neutrino-flavor conversion (FFC),
paying special attention to asymptotic states, by linear stability analysis and
local simulations with a periodic boundary condition. We find that asymptotic
states can be characterized by two key properties of FFC: (1) the conservation
of lepton number for each flavor of neutrinos and (2) the disappearance of
ELN(electron neutrino-lepton number)-XLN(heavy-leptonic one) angular crossings
in the spatial- or time-averaged distributions. The system which initially has
the positive (negative) ELN-XLN density reaches a flavor equipartition in the
negative (positive) ELN-XLN angular directions, and the other part compensates
it to preserve the conservation laws. These properties of FFCs offer an
approximate scheme determining the survival probability of neutrinos in
asymptotic states without solving quantum kinetic equations. We also
demonstrate that the total amount of flavor conversion can vary with
species-dependent neutrino distributions for identical ELN-XLN ones. Our
results suggest that even shallow or narrow ELN angular crossings have the
ability to drive large flavor conversion, exhibiting the need for including the
effects of FFCs in the modeling of CCSN and BNSM.
