Small C^s perturbations of generic volume-preserving 3D Anosov flow time-1 maps make smooth measures converge exponentially to a unique full-support limit, implying stable transitivity and unique physical measures.
[Wil] Wilkinson, A.,Conservative partially hyperbolic dynamics,Proceedings of the International Congress of Mathematicians
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Perturbation of the time-1 map of a generic volume-preserving $3$-dimensional Anosov flow
Small C^s perturbations of generic volume-preserving 3D Anosov flow time-1 maps make smooth measures converge exponentially to a unique full-support limit, implying stable transitivity and unique physical measures.