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 …

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 …

Various diagnostics of the emergence of an arrow of time in the bulk description of a
holographic theory have been proposed, including the decay of some real time correlation …

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 …

The known examples of transitive partially hyperbolic diffeomorphisms on 3-manifolds
belong to 3 basic classes: perturbations of skew products over an Anosov map of T2 …

ON DYNAMICS OF MOSTLY CONTRACTING DIFFEOMORPHISMS. 1. Introduction. This
paper treats a class of partially hyperbolic systems wi Page 1 ON DYNAMICS OF MOSTLY …

We prove that in the space of all Cr (r⩾ 1) partially hyperbolic dif-feomorphisms, there is a
C1 open and dense set of accessible diffeomorphisms. This settles the C1 case of a …