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arXiv · 2203.12017

A Rokhlin Lemma for Noninvertible Totally-Ordered Measure-Preserving Dynamical Systems

Adam R. B. Erickson
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Abstract

Let $(X,\mathcal{F},\mu,T)$ be a not necessarily invertible non-atomic measure-preserving dynamical system where the $\sigma$-algebra $\mathcal{F}$ is generated by the intervals according to some total order. The main result is that the classical Rokhlin lemma may be adapted to such a situation assuming a slight extension of aperiodicity. This result is compared to previous noninvertible versions of the Rokhlin lemma.

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Adam R. B. Erickson. 2022-03-22. A Rokhlin Lemma for Noninvertible Totally-Ordered Measure-Preserving Dynamical Systems. https://arxiv.org/abs/2203.12017

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