Exponential mixing implies Bernoulli

Dmitry Dolgopyat; Adam Kanigowski; Federico Rodriguez Hertz

doi:https://doi.org/10.4007/annals.2024.199.3.5

Pages 1225-1292 from Volume 199 (2024), Issue 3 by Dmitry Dolgopyat, Adam Kanigowski, Federico Rodriguez Hertz

Abstract

Let $f$ be a $C^{1+\alpha}$ diffeomorphism of a compact manifold $M$ preserving a smooth measure $\mu$. We show that if $f\colon (M,\mu)\to (M,\mu)$ is exponentially mixing, then it is Bernoulli.

Mathematical Subject Classification

Primary 2020: 37A35, 37D25 Secondary: 37A25

Milestones

Received: 11 June 2021
Revised: 8 December 2023
Accepted: 11 December 2023
Published online: 1 May 2024

Authors

Dmitry Dolgopyat

University of Maryland, College Park, MD, USA

Adam Kanigowski

University of Maryland, College Park, MD, USA and Jagiellonian University, Łojasiewicza 6, Kraków, Poland

Federico Rodriguez Hertz

The Pennsylvania State University, University Park, PA, USA