  The low-energy modes of a superfluid atomic Fermi gas at zero temperature are
investigated. The Bose-Einstein-condensate (BEC) side of the superfluid phase
is studied in detail. The atoms are assumed to be in only one internal state,
so that for a sufficiently diluted gas the pairing of fermions can be
considered effective in the l=1 channel only. In agreement with previous works
on p-wave superfluidity in Fermi systems, it is found that the $p_x+ip_y$ phase
represents the lowest energy state in both the Bardeen-Cooper-Schrieffer (BCS)
and BEC sides. Our calculations show that at low energy three branches of
collective modes can emerge, with different species of dispersion relations: a
phonon-like mode, a single-particle-like mode and a gapped mode. A comparison
with the Bogoliubov excitations of the corresponding spinor Bose condensate is
made. They reproduce the dispersion relations of the excitation modes of the
p-wave superfluid Fermi gas to a high accuracy.
