By using the variational approach, we prove the existence of Sinai–Ruelle–Bowen measures for partially hyperbolic C¹ diffeomorphisms with mostly expanding properties. The same conclusion holds true if one considers a dominated splitting E⊕ F, where dim E=1 and F is mostly expanding. When the diffeomorphisms are C1+α, we prove the basin covering property for both cases.
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Burguet et al. (2025) studied this question.
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