Backward inducing and exponential decay of correlations for partially hyperbolic attractors

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How researchers see this paper

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Averaging and Invariant Measures (2005, unknown): “Mostly contracting diffeomorphisms has been studied in [6], [9], [10], [11], [16], [42] and their properties are well understood.”
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].”
Physical measures and absolute continuity for one-dimensional center direction (2013, background): “Short afterwards, Castro [30] and Dolgopyat [31] proved exponential decay of correlations and other ergodic properties for certain diffeomorphisms with mostly contracting center.”