Exponential mixing implies Bernoulli

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.

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