# Unique ergodicity and zero entropy of irregular almost automorphic symbolic extensions of irrational rotations

 Dia 2018-11-30 14:30:00-03:00 Hora 2018-11-30 14:30:00-03:00 Lugar Salón de seminarios del IMERL, Facultad de Ingeniería

### Unique ergodicity and zero entropy of irregular almost automorphic symbolic extensions of irrational rotations

#### Dr. Gabriel Fuhrmann(Imperial College, London)

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 a particular Cantor set, we prove that for each irrational rotation there still are such almost automorphic extensions which are mean-equicontinuous (and hence have zero entropy and are uniquely ergodic). We will shortly review the results by Markley and Paul and then discuss the construction of the Cantor set