  We show that time-one maps of transitive Anosov flows of compact manifolds
are accumulated by diffeomorphisms robustly satisfying the following dichotomy:
either all of the measures of maximal entropy are non-hyperbolic, or there are
exactly two ergodic measures of maximal entropy, one with a positive central
exponent and the other with a negative central exponent.
  We establish this dichotomy for certain partially hyperbolic diffeomorphisms
isotopic to the identity whenever both of their strong foliations are minimal.
Our proof builds on the approach developed by Margulis for Anosov flows where
he constructs suitable families of measures on the dynamical foliations.
