Several distinctive aspects make Dynamical Systems unique, including: treating the subject
from a mathematical perspective with the proofs of most of the results includedproviding a …

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 …

1. Introduction. It is the goal ofthis paper to estimate the regularity of the holonomy maps of
certain dynamically invariant foliations. They are 0-H61der. This H61der regularity is a …

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 …

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 …

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In this paper we show that a little hyperbolicity goes a long way toward guaranteeing stable
ergodicity, and in fact may be necessary for it. Our main theorem may be interpreted as …