In this talk, we introduce the class of irreducible discretized Anosov flows and study their measures of maximal entropy. We show that such systems always admit a unique ergodic measure maximizing entropy along the unstable (respectively, stable) foliation. Generically, the ergodic measure that maximizes entropy along the unstable foliation differs from the one that maximizes entropy along the stable foliation, and these are the only ergodic measures of maximal entropy.

Our approach relies on constructing conformal measures along the leaves of invariant foliations, extending Margulis’s construction for the time-one map of Anosov flows.

This is a joint work with Jérôme Buzzi, Sylvain Crovisier and Mauricio Poletti.