Ergodic Properties of Measures with Local Product Structure

2022/06/05 by Nawaf Alansari, Alansari, Nawaf
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2206.02242

openalex publication_date 2022/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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