In broad terms, the goal of dynamics is to describe the long-term evolution of systems for
which an" infinitesimal" evolution rule, such as a differential equation or the iteration of a …

We show that, for every compact n-dimensional manifold, n> 1, there is a residual subset of
Diff (M) of diffeomorphisms for which the homoclinic class of any periodic saddle of f verifies …

This book is an introduction to the modern theory of partial hyperbolicity with applications to
stable ergodicity theory of smooth dynamical systems. It provides a systematic treatment of …

We consider a large class of partially hyperbolic systems containing, among others, affine
maps, frame flows on negatively curved manifolds, and mostly contracting diffeomorphisms …

Pugh and Shub have conjectured that essential accessibility implies ergodicity for a C 2,
partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a …

We propose a new approach to analyzing dynamical systems that combine hyperbolic and
non-hyperbolic (“center”) behavior, eg partially hyperbolic diffeomorphisms. A number of …

The ergodic theory of uniformly hyperbolic, or “Axiom A”, diffeomorphisms has been studied
extensively, beginning with the pioneering work of Anosov, Sinai, Ruelle and Bowen …

We prove that stable ergodicity is C r open and dense among conservative partially
hyperbolic diffeomorphisms with one-dimensional center bundle, for all r in [2, infty]. The …

We study compact group extensions of hyperbolic diffeomorphisms. We relate mixing
properties of such extensions with accessibility properties of their stable and unstable …

In this paper we dramatically expand the domain of known stably ergodic, partially
hyperbolic dynamical systems. For example, all partially hyperbolic affine diffeomorphisms …