Furstenberg's topological x2 x3 result
Speaker: Barak Weiss
Date: Tue, Aug 16, 2022
Location: University of Utah, Zoom
Conference: Online working seminar in Ergodic Theory, University of Utah Seminar in Ergodic Theory
Subject: Mathematics
Class: Scientific
Date: Tue, Aug 16, 2022
Location: University of Utah, Zoom
Conference: Online working seminar in Ergodic Theory, University of Utah Seminar in Ergodic Theory
Subject: Mathematics
Class: Scientific
Abstract:
In 1967 Furstenberg proved that any closed subset of the one dimensional torus R/Z, invariant under the two maps x -> 2x mod 1, x -> 3x mod 1, is either finite or the entire torus. I will explain a proof of this result due to Boshernitzan (1994). Furstenberg's proof is slightly longer but perhaps more conceptual. I will explain the main steps in Furstenberg's approach and their connection to joinings.
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