Physical measures on partially hyperbolic diffeomorphisms with multi 1-D centers

In this paper, we study physical measures for partially hyperbolic diffeomorphisms with multi one-dimensional centers under the condition that all Gibbs $u$-states are hyperbolic. First, we prove the finiteness of ergodic physical measures. By building a criterion, we then obtain the basin covering property for ergodic physical measures under some restriction on the sign of Lyapunov exponents with respect to empirical measures.