Ergodicity of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds

Transitive Partially Hyperbolic Diffeomorphisms on 3-Manifolds

Classification of Partially Hyperbolic Diffeomorphisms in 3-manifolds with Solvable Fundamental Group

A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus, it is dynamically coherent and leaf conjugate to a known algebraic example. This classification includes manifolds which support Anosov flows, and it confirms...

On the ergodicity of partially hyperbolic systems

Pugh and Shub [PS3] have conjectured that essential accessibility implies ergodicity, for a C2, partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a mild center bunching assumption, which is satsified by all partially hyperbolic systems with 1-dimensional center bundle. We also obtain ergodicity results for C1+γ partially hyperbolic systems.

Partially Hyperbolic Diffeomorphisms with a Trapping Property

We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an expansive quotient of the dynamics and study some dynamical consequences related to this quotient.

The Cohomological Equation for Partially Hyperbolic Diffeomorphisms

Introduction 2 1. Techniques in the proof of Theorem A 7 2. Partial hyperbolicity and bunching conditions 10 2.1. Notation 11 3. The partially hyperbolic skew product associated to a cocycle 12 4. Saturated sections of admissible bundles 13 4.1. Saturated cocycles: proof of Theorem A, parts I and III 18 5. Hölder regularity: proof of Theorem A, part II. 21 6. Jets 28 6.1. Prolongations 29 6.2. ...