In this talk we will prove a dichotomy for the cardinality of ergodic measures of maximal entropy and their hyperbolicity for a class of partially hyperbolic diffeomorphisms denoted by Irreducible Discretized Anosov flows.
In particular we conclude that generically ( in fact C1-open and C^\infty-dense) discretized Anosov flows admit exactly two ergodic measures of maximal entropy, both hyperbolic and with exponential decay of correlation. This is a joint work with J. Buzzi, S. Crovisier and M. Poletti. | 
