Measures of maximal u-entropy for maps that factor over Anosov

This is a joint work with Raul Ures, Marcelo Viana and Fan Yang. We construct measures of maximal u-entropy for any partially hyperbolic diffeomorphism that factors over an Anosov torus automorphism and has mostly contracting center direction. The space of such measures has a finite dimension, and its extreme points are ergodic measures with pairwise disjoint supports.