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Anomalous Anosov flows revisited

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arxiv 1712.07755 v1 pith:MAZUQPOO submitted 2017-12-21 math.DS math.GT

Thomas Barthelmé , Christian Bonatti , Andrey Gogolev , Federico Rodriguez Hertz This is my paper · ORCID
classification math.DSmath.GT
keywords anosovflowsdimensionaldimensionspartaffineanomalousbundles
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This paper is devoted to higher dimensional Anosov flows and consists of two parts. In the first part, we investigate fiberwise Anosov flows on affine torus bundles which fiber over 3-dimensional Anosov flows. We provide a dichotomy result for such flows --- they are either suspensions of Anosov diffeomorphisms or the stable and unstable distributions have equal dimensions. In the second part, we give a new surgery type construction of Anosov flows, which yields non-transitive Anosov flows in all odd dimensions.

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  1. Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part I: The dynamically coherent case

    math.DS 2019-08 conditional novelty 8.0 of 10

    On hyperbolic and Seifert fibered 3-manifolds, dynamically coherent partially hyperbolic diffeomorphisms homotopic to the identity are, up to iterate, leaf conjugate to time-one maps of topological Anosov flows.

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