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Ergodicity of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds

Research paper by Sergio Fenley, Rafael Potrie

Indexed on: 06 Sep '18Published on: 06 Sep '18Published in: arXiv - Mathematics - Dynamical Systems



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.