SRB Measures for Mostly Expanding Partially Hyperbolic Diffeomorphisms via the Variational Approach

Abstract By using the variational approach, we prove the existence of Sinai–Ruelle–Bowen measures for partially hyperbolic $\mathcal C^{1}$ diffeomorphisms with mostly expanding properties. The same conclusion holds true if one considers a dominated splitting $E\oplus F$, where $\operatorname{dim} E=1$ and $F$ is mostly expanding. When the diffeomorphisms are $\mathcal C^{1+\alpha }$, we prove the basin covering property for both cases.