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arXiv · 1508.02817

On doubly minimal systems and a question regarding product recurrence

Eli Glasner·Benjamin Weiss
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Abstract

We show that a doubly minimal system $X$ has the property that for every minimal system $Y$ the orbit closure of any pair $(y,x) \in Y \times X$ is either $Y \times X$ or it has the form $\Gamma_\pi = \{(\pi(x),x) : x \in X\}$ for some factor map $\pi: X \to Y$. As a corollary we resolve a problem of Haddad and Ott from 2008 regarding product recurrence.

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Eli Glasner, Benjamin Weiss. 2015-08-12. On doubly minimal systems and a question regarding product recurrence. https://arxiv.org/abs/1508.02817

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