Gabriel Fuhrmann (Imperial College): Unique ergodicity and zero entropy of irregular symbolic extensions of irrational rotations.

Abstract: A classical result by Markley and Paul states that irregular almost automorphic systems over irrational rotations are typically not uniquely ergodic and have positive entropy. By constructing particular Cantor sets, we prove that for each irrational rotation there still are almost automorphic extensions which are mean-equicontinuous (and hence have zero entropy and are uniquely ergodic). The goal of the talk is to shortly review the results by Markley and Paul and then discuss the construction of the mentioned Cantor sets. This is a joint work with Eli Glasner, Tobias Jäger and Christian Oertel.