  Here we investigate the axial w quasi-normal modes of neutron stars for
several equations of state. In particular, we study the influence of the
presence of hyperons in the core of the neutron stars. We have obtained that
w-modes can be used to distinguish between neutron stars with hyperons and
without hyperons for compact enough stars. We present phenomenological
relations for the frequency and damping times with the compactness of the
neutron star for wI and wII modes showing the differences of the stars with
hyperons in the core. Also, we obtain a new phenomenological relation between
the real part and the imaginary part of the frequency of the w quasi-normal
modes, which can be used to estimate the central pressure of the neutron stars.
We are able to construct explicitly the low compactness limit configuration for
which the fundamental wII mode vanishes. Finally, we have studied the influence
of changes in the core-crust transition pressure obtaining that it is very
small. To obtain these results we have developed a new method based on the
Exterior Complex Scaling technique with variable angle, appropriate for the
treatment of the exterior part of the quasi-normal modes, which allow us to
impose constringent enough conditions to generate pure outgoing quasi-normal
modes. For the interior part we use a piece-wise polytrope approximation for
several equations of state. A complete study of the junction conditions have
been done.
