Ergodicity of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds

DOI10.1016/J.AIM.2022.108315arXiv1809.02284WikidataQ115598692 ScholiaQ115598692MaRDI QIDQ6306365

Publication date: 6 September 2018

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.

Mathematics Subject Classification ID

Foliations in differential topology; geometric theory (57R30) Partially hyperbolic systems and dominated splittings (37D30) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Hyperbolic 3-manifolds (57K32)

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