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.
V .,Geodesic flows on closed Riemann manifolds with negative curvature,Proceedings of the Steklov Insti- tute of Mathematics, No.90(1967), 3-210; Translated from the Russian by S
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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.