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Ergodicity of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds

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arxiv 1809.02284 v3 pith:HNBMNE4T submitted 2018-09-07 math.DS math.GT

Sergio Fenley , Rafael Potrie This is my paper · ORCID
classification math.DSmath.GT
keywords hyperbolicpartiallydiffeomorphismsmanifoldsconservativeaccessibleafirmativealways
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abstract

We study conservative partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds. We show that they are always accessible and deduce as a result that every conservative $C^{1+}$ partially hyperbolic in a hyperbolic 3-manifold must be ergodic, giving an afirmative answer to a conjecture of Hertz-Hertz-Ures in the context of hyperbolic 3-manifolds. Some of the intermediary steps are also done for general partially hyperbolic diffeomorphisms homotopic to the identity.

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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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