Variation of measures of maximal $ u $-entropy

In this paper, we study the variation of ergodic measures of maximal $ u $-entropy among the set of diffeomorphisms factoring over Anosov and having $ c $-mostly contracting center. By using the concept of skeleton introduced in [6] we prove that the number of such measures is upper semi-continuous in the $ C^1 $-topology. We also give an example to show how these measures collapse under small perturbations.