Ergodicity of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds

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.

43 pages, 4 figures. To appear in Advances in Math

Cited by in corpus (1)

• Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part II: Branching foliations