  Intermediate energy heavy ion collisions open the unique possibility to
explore the Equation of State ($EOS$) of nuclear matter far from saturation, in
particular the density dependence of the symmetry energy. Within a relativistic
transport model it is shown that the isovector-scalar $\delta$-meson, which
affects the high density behavior of the symmetry energy density, influences
the dynamics of heavy ion collisions in terms of isospin collective flows. The
effect is largely enhanced by a relativistic mechanism related to the covariant
nature of the fields contributing to the isovector channel. Results for
reactions induced by $^{132}Sn$ radioactive beams are presented. The elliptic
flows of nucleons and light isobars appear to be quite sensitive to microscopic
structure of the symmetry term, in particular for particles with large
transverse momenta, since they represent an earlier emission from a compressed
source. Thus future, more exclusive, experiments with relativistic radioactive
beams should be able to set stringent constraints on the density dependence of
the symmetry energy far from ground state nuclear matter.
