Ergodic Properties of Measures with Local Product Structure

TL;DR

This paper investigates ergodic properties of hyperbolic measures with local product structure, extending classical results like ergodic decomposition and Bernoulli property to these measures.

Contribution

It demonstrates that classical ergodic results apply to hyperbolic measures with local product structure, including decomposition and K- to Bernoulli properties.

Findings

Decomposition into countably many ergodic components

K-property implies Bernoulli property for these measures

Examples illustrating applicability of the results

Abstract

In this paper, we study ergodic properties of hyperbolic measures with local product structure. We show that all the classical results that hold in the case of SRB measure hold for these measures. In particular, we show the decomposition in countably many ergodic components, we prove the decomposition into K-components, and show that for hyperbolic measure with local product structure, The K property implies the Bernoulli property. We also give some examples of measures where the results are applicable.