This paper surveys recent results on classifying partially hyperbolic diffeomorphisms. This
includes the construction of branching foliations and leaf conjugacies on three-dimensional …

These are notes for a minicourse in the School on Dynamical Systems 2015 at ICTP. This
version is quite preliminary, incomplete (mainly in the last sections) and probably contains …

In this paper we obtain local rigidity results for linear Anosov diffeomorphisms in terms of
Lyapunov exponents. More specifically, we show that given an irreducible linear hyperbolic …

We prove that dynamical coherence is an open and closed property in the space of partially
hyperbolic diffeomorphisms of $\mathbb {T}^ 3$ isotopic to Anosov. Moreover, we prove that …

Let $\mathcal {F} _1 $ and $\mathcal {F} _2 $ be transverse two dimensional foliations with
Gromov hyperbolic leaves in a closed 3-manifold $ M $ whose fundamental group is not …

We discover a rigidity phenomenon within the volume-preserving partially hyperbolic
diffeomorphisms with 1-dimensional center. In particular, for smooth ergodic perturbations of …

We construct examples of robustly transitive and stably ergodic partially hyperbolic
diffeomorphisms f on compact 3-manifolds with fundamental groups of exponential growth …

A deep analysis of the Lyapunov exponents for stationary sequence of matrices going back
to Furstenberg, for more general linear cocycles by Ledrappier, and generalized to the …

We show that partially hyperbolic diffeomorphisms of d d-dimensional tori isotopic to an
Anosov diffeomorphism, where the isotopy is contained in the set of partially hyperbolic …

A classification of partially hyperbolic diffeomorphisms on three-dimensional manifolds with
(virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a …