  High energy Heavy Ion Collisions (HIC) are studied in order to access nuclear
matter properties at high density. Particular attention is paid to the
selection of observables sensitive to the poorly known symmetry energy at high
baryon density, of large fundamental interest, even for the astrophysics
implications. Using fully consistent transport simulations built on effective
theories we test isospin observables ranging from nucleon/cluster emissions to
collective flows (in particular the elliptic, squeeze out, part). The effects
of the competition between stiffness and momentum dependence of the Symmetry
Potential on the reaction dynamics are thoroughly analyzed. In this way we try
to shed light on the controversial neutron/proton effective mass splitting at
high baryon and isospin densities. New, more exclusive, experiments are
suggested.
