  We discuss, in an investigation based on Vlasov equation, the properties of
the isovector modes in nuclear matter and atomic nuclei in relation with the
symmetry energy. We obtain numerically the dipole response and determine the
strength function for various systems, including a chain of Sn isotopes. We
consider for the symmetry energy three parametrizations with density providing
similar values at saturation but which manifest very different slopes around
this point. In this way we can explore how the slope affects the collective
response of finite nuclear systems. We focus first on the dipole polarizability
and show that while the model is able to describe the expected mass dependence,
A^{5/3}, it also demonstrates that this quantity is sensitive to the slope
parameter of the symmetry energy. Then, by considering the Sn isotopic chain,
we investigate the emergence of a collective mode, the Pygmy Dipole Resonance
(PDR), when the number of neutrons in excess increases. We show that the total
energy-weighted sum rule exhausted by this mode has a linear dependence with
the square of isospin I=(N-Z)/A, again sensitive to the slope of the symmetry
energy with density. Therefore the polarization effects in the isovector
density have to play an important role in the dynamics of PDR. These results
provide additional hints in the investigations aiming to extract the properties
of symmetry energy below saturation.

Nuclear Theory;Nuclear Experiment