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arXiv · 2009.10566

On the multiple recurrence properties for disjoint systems

Michihiro Hirayama·Dong Han Kim·Younghwan Son
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Abstract

We consider mutually disjoint family of measure preserving transformations $T_1, \cdots, T_k$ on a probability space $(X, \mathcal{B}, \mu)$. We obtain the multiple recurrence property of $T_1, \cdots, T_k$ and this result is utilized to derive multiple recurrence of Poincar\'e type in metric spaces. We also present multiple recurrence property of Khintchine type. Further, we study multiple ergodic averages of disjoint systems and we show that $T_1, \cdots, T_k$ are uniformly jointly ergodic if each $T_i$ is ergodic.

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Michihiro Hirayama, Dong Han Kim, Younghwan Son. 2020-09-22. On the multiple recurrence properties for disjoint systems. https://arxiv.org/abs/2009.10566

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