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 …

Consider a one parameter family of diffeomorphisms f ε such that f 0 is an Anosov element in
a standard abelian Anosov action having sufficiently strong mixing properties. Let ν ε be any …

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 …

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

Vector fields whose flow preserves a symplectic form up to a constant, such as simple
mechanical systems with friction, are called “conformal”. We develop a reduction theory for …