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Let $f$ be a $C^2$ diffeomorphism on compact Riemannian manifold $M$ withpartially hyperbolic splitting $$ TM=E^u\oplus E_1^c\oplus\cdots\oplus E_k^c\oplus E^s, $$ where $E^u$ is uniformly expanding, $E^s$ is uniformlycontracting, and ${\rm dim}E_i^c=1,~ 1\le i \le k, ~k\ge 1$. We prove thefiniteness of ergodic physical(SRB) measures of $f$ under the hyperbolicity ofGibbs $u$-states.

Finiteness of physical measures for diffeomorphisms with multi 1-D centers