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.
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Under compact support, gap, pinching, and weak-* proximity to volume-preservation, random walks by C² diffeomorphisms on a closed manifold M admit a unique atom-free stationary measure Υ_μ of full Frostman dimension to which μ^{*n} * δ_x converges for most x.
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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.
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Rigidity and equidistribution of random walks by diffeomorphisms near the conservative regime
Under compact support, gap, pinching, and weak-* proximity to volume-preservation, random walks by C² diffeomorphisms on a closed manifold M admit a unique atom-free stationary measure Υ_μ of full Frostman dimension to which μ^{*n} * δ_x converges for most x.