Every ergodic transformation is disjoint from almost every interval exchange transformation

Abstract

We show that every transformation is disjoint from almost every interval exchange transformation (IET), answering a question of Bufetov. In particular, we prove that almost every pair of IETs is disjoint. It follows that the product of almost every pair is uniquely ergodic. A key step in the proof is showing that any sequence of density 1 contains a rigidity sequence for almost every IET, strengthening a result of Veech.

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Authors

Jon Chaika

Department of Mathematics
University of Chicago
5734 University Avenue
Chicago, IL 60637