On the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with compact center leaves

In this paper we study the number of ergodic measures maximal entropy for partially hyperbolic diffeomorphisms defined on 3-torus with compact center leaves. Assuming existence a periodic leaf Morse–Smale dynamics prove sharp upper bound in terms sources and sinks dynamics. A well-known class examples which our results apply are so called Kan-type admitting physical intermingled basins.