Smooth mixing transformations with loosely Bernoulli cartesian product

2019/12/24 by Frank Trujillo, Trujillo, Frank
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1912.11445

openalex publication_date 2019/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A zero-entropy system is said to be loosely Bernoulli if it can be induced from an irrational rotation of the circle. We provide a criterion for zero-entropy systems to be loosely Bernoulli that is compatible with mixing. Using these criteria, we show the existence of smooth mixing zero-entropy loosely Bernoulli transformations whose cartesian product with themselves is loosely Bernoulli.

Citations

• On Groups of Measure Preserving Transformations. I

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