Anomalous partially hyperbolic diffeomorphisms III: Abundance and incoherence

Anomalous partially hyperbolic diffeomorphisms I: dynamically coherent examples

We build an example of a non-transitive, dynamically coherent partially hyperbolic diffeomorphism f on a closed 3-manifold with exponential growth in its fundamental group such that f is not isotopic to the identity for all n ̸= 0. This example contradicts a conjecture in [HHU1]. The main idea is to consider a well-understood time-t map of a non-transitive Anosov flow and then carefully compose ...

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. ...

Transitive Partially Hyperbolic Diffeomorphisms on 3-Manifolds

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.