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On decay of correlations in Anosov flows

- D. Dolgopyat
- Mathematics
- 1 March 1998

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… Expand

Prevalence of rapid mixing in hyperbolic flows

- D. Dolgopyat
- Mathematics
- 1 October 1998

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… Expand

Brownian Brownian Motion-I

- N. Chernov, D. Dolgopyat
- Mathematics, Physics
- 29 November 2008

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… Expand

On mixing properties of compact group extensions of hyperbolic systems

- D. Dolgopyat
- Mathematics
- 1 December 2002

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… Expand

On Dynamics of Mostly Contracting Diffeomorphisms

- D. Dolgopyat
- Physics
- 1 September 2000

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

- D. Dolgopyat
- Mathematics
- 22 September 2003

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… Expand

Stable accessibility is C1 dense

- D. Dolgopyat, A. Wilkinson
- Mathematics
- 2001

— 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… Expand

Averaging and Invariant Measures

- D. Dolgopyat
- Mathematics
- 2005

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… Expand

Prevalence of rapid mixing—II: topological prevalence

- D. Dolgopyat
- MathematicsErgodic 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),… Expand

On differentiability of SRB states for partially hyperbolic systems

- D. Dolgopyat
- Mathematics
- 1 February 2004

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… Expand

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