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.
[KK] Kalinin, B., Katok, A.,Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori, Journal of Modern Dynamics, V ol.1, No
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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.