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 construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of
diffeomorphisms–the tangent bundle splits into two invariant subbundles, one of which is …

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 …

This article surveys results and conjectures in dynamical systems and other areas that
describe properties of 'almost every'function in some space, using a probabilistic (or …

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 …

We consider zero-noise limits of random perturbations of dynamical systems and examine,
in terms of the continuity of entropy and Lyapunov exponents, circumstances under which …

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

Robust chaos is defined by the absence of periodic windows and coexisting attractors in
some neighborhoods in the parameter space of a dynamical system. This unique book …