Topological quasi-stability of partially hyperbolic diffeomorphisms under random perturbations

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.

A Note on Minimality of Foliations for Partially Hyperbolic Diffeomorphisms

It was shown that in robustly transitive, partially hyperbolic diffeomorphisms on three dimensional closed manifolds, the strong stable or unstable foliation is minimal. In this article, we prove “almost all” leaves of both stable and unstable foliations are dense in the whole manifold.