  We consider a Fermi liquid model with density-density as well as quadrupolar
forward scattering interactions parametrized by the Landau parameters $F_0$ and
$F_2$. Using bosonization and a decimation technique, we compute collective
modes and spectral functions for a huge range of interactions, ranging from
strong repulsion to strong attraction in either angular momentum channels. We
present a dynamical phase diagram showing a region of parameters where the
collective modes structure changes abruptly, possibly signaling a dynamical
phase transition.
