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Hyperbolic models of transitive topologically Anosov flows in dimension three

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arxiv 2108.12000 v2 pith:FBE3UQPL submitted 2021-08-26 math.DS

Mario Shannon This is my paper · ORCID
classification math.DS
keywords anosovflowsmoothtopologicallytransitivecloseddimensionequivalent
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We prove that every transitive topologically Anosov flow on a closed 3-manifold is orbitally equivalent to a smooth Anosov flow, preserving an ergodic smooth volume form.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three

    math.DS 2025-05 conditional novelty 8.0 of 10

    Conservative partially hyperbolic diffeomorphisms homotopic to the identity on closed 3-manifolds with non-virtually-solvable fundamental group are always accessible and hence ergodic.

  2. Pseudo-Anosov flows on hyperbolic L-spaces

    math.GT 2025-05 accept novelty 8.0 of 10

    For every even n≥4, infinitely many surgeries on the n-chain link are hyperbolic L-spaces with n orbit-inequivalent pseudo-Anosov flows and n universally tight non-contactomorphic contact structures.

  3. Topological invariance of Liouville structures for taut foliations and Anosov flows

    math.SG 2025-10 conditional novelty 7.0 of 10

    Topologically conjugate taut foliations and orbit-equivalent Anosov flows produce exact symplectomorphic Liouville thickenings; the smoothing method also yields new collapsed Anosov flows.

  4. Partially Hyperbolic Dynamics with Quasi-isometric Center

    math.DS 2024-11 conditional novelty 7.0 of 10

    Non-wandering partially hyperbolic diffeomorphisms with quasi-isometric center on closed 3-manifolds are either skew products over a torus Anosov map or discretized Anosov flows, and volume-preserving ones are ergodic.

  5. Quasi-isometric center action in dimension 3

    math.DS 2024-11 conditional novelty 7.0 of 10

    Transitive partially hyperbolic diffeomorphisms in dimension 3 that act quasi-isometrically on an invariant center foliation are classified up to finite lift and iterate as skew-products or discretised Anosov flows.

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