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On decay of correlations in Anosov flows
There is some disagreement about the meaning of the phrase 'chaotic flow.' However, there is no doubt that mixing Anosov flows provides an example of such systems. Anosov systems were introduced and
Prevalence of rapid mixing in hyperbolic flows
We provide necessary and sufficient conditions for a suspension flow, over a subshift of finite type, to mix faster than any power of time. Then we show that these conditions are satisfied if the
Brownian Brownian Motion-I
A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work the authors study a 2D version of this model, where the
On mixing properties of compact group extensions of hyperbolic systems
We study compact group extensions of hyperbolic diffeomorphisms. We relate mixing properties of such extensions with accessibility properties of their stable and unstable laminations. We show that
On Dynamics of Mostly Contracting Diffeomorphisms
Abstract:Mostly contracting diffeomorphisms are the simplest examples of robustly nonuniformly hyperbolic systems. This paper studies the mixing properties of mostly contracting diffeomorphisms.
Limit theorems for partially hyperbolic systems
We consider a large class of partially hyperbolic systems containing, among others, affine maps, frame flows on negatively curved manifolds, and mostly contracting diffeomorphisms. If the rate of
Stable accessibility is C1 dense
— We prove that in the space of ail Cr (r ^ 1) partially hyperbolic diffeomorphisms, there is a C1 open and dense set of accessible diffeomorphisms. This settles the C1 case of a conjecture of Pugh
Averaging and Invariant Measures
An important approach to establishing stochastic behavior of dynamical systems is based on the study of systems expanding a foliation and of measures having smooth densities along the leaves of this
Prevalence of rapid mixing—II: topological prevalence
  • D. Dolgopyat
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 1 August 2000
We continue the study of mixing properties of generic hyperbolic flows started in an earlier paper (D. Dolgopyat. Prevalence of rapid mixing in hyperbolic flows. Erg. Th.& Dyn. Sys.18 (1998),
On differentiability of SRB states for partially hyperbolic systems
Consider a one parameter family of diffeomorphisms fε such that f0 is an Anosov element in a standard abelian Anosov action having sufficiently strong mixing properties. Let νε be any u-Gibbs state