The Bernoulli property of Sinai-Ruelle-Bowen measures for flows

TL;DR

This paper proves that certain hyperbolic SRB measures for specific flows with singularities exhibit Bernoulli properties, extending understanding of their statistical behavior.

Contribution

It establishes Bernoulli properties for weakly mixing hyperbolic SRB measures in flows with singularities, a novel extension in dynamical systems theory.

Findings

Hyperbolic SRB measures are Bernoulli for flows with singularities.

Weakly mixing hyperbolic measures exhibit Bernoulli properties.

Results apply to $C^{1+eta}$ flows with singularities.

Abstract

We prove that for $C^{1+\beta}$ flows whose generating vector fields may have singularities, every weakly mixing hyperbolic SRB measure is Bernoullian.