On codimension one partially hyperbolic diffeomorphisms

Transitive Partially Hyperbolic Diffeomorphisms on 3-Manifolds

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.

On Structurally Stable Diffeomorphisms with Codimension One Expanding Attractors

We show that if a closed n-manifold Mn (n ≥ 3) admits a structurally stable diffeomorphism f with an orientable expanding attractor Ω of codimension one, then Mn is homotopy equivalent to the n-torus Tn and is homeomorphic to Tn for n 6= 4. Moreover, there are no nontrivial basic sets of f different from Ω. This allows us to classify, up to conjugacy, structurally stable diffeomorphisms having ...

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. ...

Entropy-expansiveness for Partially Hyperbolic Diffeomorphisms

We show that diffeomorphisms with a dominated splitting of the form Es⊕Ec⊕Eu, where Ec is a nonhyperbolic central bundle that splits in a dominated way into 1-dimensional subbundles, are entropy-expansive. In particular, they have a principal symbolic extension and equilibrium states.