Physical measures and absolute continuity for one-dimensional center direction

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SRB measures for partially hyperbolic systems whose central direction is weakly expanding (2014, unknown): “Additional results include conditions which imply uniqueness of the SRB measure for a diffeomor-phism and its perturbations [18, 19, 48], mixing properties of this measure [20, 21, 25], and even differentiability with respect to perturbations [26].”
Entropy along expanding foliations (2016, background): “As a corollary of the semi continuation of the set of Gibbs u-states in the C topology, the set of partially hyperbolic diffeomorphisms with mostly contracting center forms a C open set (see [12, 1, 33, 16]).”