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Accessibility and ergodicity for collapsed Anosov flows

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arxiv 2103.14630 v1 pith:AZGVBM3O submitted 2021-03-26 math.DS math.GT

Sergio R. Fenley , Rafael Potrie This is my paper · ORCID
classification math.DSmath.GT
keywords classcontainssystemsaccessibilityaccessibleadditionanosovclosed
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We consider a class of partially hyperbolic diffeomorphisms introduced in [BFP] which is open and closed and contains all known examples. If in addition the diffeomorphism is non-wandering, then we show it is accessible unless it contains a su-torus. This implies that these systems are ergodic when they preserve volume, confirming a conjecture by Hertz-Hertz-Ures for this class of systems.

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  1. 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.

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