On doubly minimal systems and a question regarding product recurrence

2015/08/12 by Glasner, Eli, Weiss, Benjamin · 1 citation
#37B05 #37B20 #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1508.02817

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) ∈ Y × X is either Y × X or it has the form Γ_π= \(π(x),x) : x ∈ X\ for some factor map π: X → Y. As a corollary we resolve a problem of Haddad and Ott from 2008 regarding product recurrence.

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