Geometry, Topology and Dynamics Seminar
Amadeus Maldonado
Northwestern University
Exponentially mixing SRB measures are Bernoulli
Abstract: The Bernoulli property is the strongest statistical property that a measure preserving system can exhibit. It not only implies other important statistical properties such as ergodicity, mixing and the K-property, but, as shown by Ornstein, Bernoulli systems with the same entropy are measurably conjugate. We prove that, for $C^{1+\alpha}$ diffeomorphisms of compact manifolds, exponentially mixing SRB measures are Bernoulli. This extends a recent result by Dolgopyat, Kanigowski and F. Rodriguez Hertz. Using similar techniques, we also show that if volume is almost exponentially mixing, then the limit SRB measure constructed by Ben Ovadia and F. Rodriguez Hertz is Bernoulli.
Wednesday September 24, 2025 at 3:00 PM in 636 SEO